Swansea chairman Huw Jenkins moved on Friday to allay fears that the club were about to lose some of their finest talent, as well as their manager, to Liverpool. However, Rodgers was decidedly more slippery when questioned on the matter.
It is hard to believe that the Swans' resolve would not be tested by any large bids and, if this is the case, then Joe Allen should be Rodgers' first port of call as Reds boss.
The 22-year-old epitomised the Welsh side's role as the surprise package in the Premier League last year - finishing as the sixth most effective passer in the sixth most effective passing side in Europe. Yes, Europe.
His age and experience, having played one short of 150 career games already, make him an almost essential addition to a Liverpool midfield which crucially struggled to control possession for so much of last season.
Though Jenkins has expressed determination to keep hold of the midfielder, there is a feeling that he would rather see him join Rodgers - with whom he enjoyed a close working relationship - should other bids arrive. Given Allen's talent and potential to get better, such interest seems likely.
With Stewart Downing and Dirk Kuyt struggling for form last year and Maxi Rodriguez and Craig Bellamy reaching the end of their careers, the Liverpool wide problem - one which has existed since Steve McManaman's departure in 1999 - is yet to be solved.
Souchaux attacker Boudebouz is a man who has been strongly linked with the Reds prior to Rodgers' arrival but recommendations from the club's scouts could mean the Northern Irishman also views him as the perfect fit.
Rodgers' penchant for using wide midfielders with the ability to cut inside, contribute goals and beat defenders in fact make the Algeria international an ideal candidate for a move to Merseyside.
The 22-year-old will have little interest in sticking around at the Ligue 1 club from whose academy he graduated given they are likely to be involved in a relegation battle again next term.
If he can build on his five goals in 32 appearances last season alongside players of the calibre of Steven Gerrard and Luis Suarez, then he might well be fighting for trophies next season.
|LUUK DE JONG|
While Dalglish faced staunch criticism for his purchases and Liverpool's poor league form last term, there was a feeling of misfortune in one aspect of his side's play - their finishing.
|FIVE PLAYERS WHO COUD LEAVE|
|Dirk Kuyt - Frustrated with a lack of appearances under Dalglish but has expressed willingness to meet the new boss.
Maxi Rodriguez - Almost certain to leave given his large salary and relatively small contribution last term.
Jay Spearing - Appeared badly out of his depth covering for Lucas Leiva last season.
Stewart Downing - Endured a torrid debut season at Anfield and may struggle given Rodgers' distaste for traditional wingers.
Jamie Carragher - Not getting any younger and criminally poor in possession at times - not something Rodgers is known to tolerate.
It is for this reason that another man who has long been linked with a switch to the red half of Merseyside could come in under Rodgers. Twente striker Luuk de Jong is reportedly being trailed by a number of English clubs, thanks to his blistering recent form in the Eredivisie.
The 21-year-old hit the net 25 times in 32 appearances in the Dutch top flight this term and is reportedly receptive to a move away, particularly to the Premier League.
His intelligent movement, eye for a goal and age make him a realistic target for Rodgers under FSG's 'Moneyball' approach and again this is a player who will come highly recommended from Liverpool's scouting network.
One potential stumbling block could come in the form of interest from Tottenham and Bayern Munich, whose superior desire to snag the Dutchman could prove decisive.
That said, the number of home draws endured by Liverpool last year mean they might just see the worth in winning a bidding war for the Netherlands international in order to alleviate their woes in front of goal.
A reported price of €15 million (£10m) would of course be viewed as a bargain should it solve the club's goalscoring issues. Whether Rodgers is convinced by a man he has not targeted himself remains to be seen but 59 goals in 119 appearances speaks for itself.
Given that midfield was an area in which Liverpool spectacularly failed for the duration of last season, it is unsurprising that they have been linked with so many talents in that position.
Gaston Ramirez is one of the latest names to be suggested, a Uruguay international colleague of Luis Suarez who has flourished in Serie A this season.
He helped Bologna to a respectable ninth-placed finish in the Italian top flight this term, scoring eight goals in 34 appearances, occupying a central role behind striker Marco Di Vaio.
The idea that he could link successfully with Suarez, as he has in the past for the current Copa America holders, must be an appealing thought to Rodgers and he is another prospect with time on his side at the age of just 21.
However, the biggest obstacle to overcome should Liverpool wish to secure the services of the former Penarol man is reported interest from Manchester City. If Roberto Mancini wishes to blow the Reds - or any other club for that matter - out of the water in terms of wages then they most certainly can.
Alternative targets will need to be sought in that case, but otherwise his price-tag of €18m (£14.5m) should fall well within Rodgers' budget.
Despite the aforementioned unwillingness of Swansea to allow Rodgers to take players with him to Liverpool, it is apparent that Sigurdsson is something of a special case.
Quite simply, the Swans do not own him, yet.
The Icelandic midfielder enjoyed a hugely impressive loan spell with the south Wales side last term, after slipping down the pecking order at German outfit Hoffenheim.
Swansea revealed this week that they had negotiated a fee with the Bundesliga side and the 22-year-old had agreed personal terms; however, with the contract apparently yet to be signed, this is far from a done deal.
Reports of the former Reading midfielder's services being secured for just £6.8m were met with widespread bemusement from those who have seen him in action in the Premier League. The idea that many of the top flight's 'bigger' clubs were unwilling to take a punt on the young and talented playmaker seemed bizarre, yet there is still time for that to happen this summer.
Sigurdsson scored seven goals in 18 league appearances last term and, with the Reds so bereft of creativity and goals in the middle - allied to Steven Gerrard's well-documented fitness issues - he could be an ideal purchase.