Any of these three players would be welcome at a club needing to beef up its squad ahead of a return to the UEFA Champions League. Either Pogba or Vidal would offer the power and drive the Reds often lacked in the middle last term.
Meanwhile, Remy's blistering pace makes him a natural fit for the lightning-fast forward line Rodgers has created. Here's the latest on these three rumours:
Arturo Vidal and Paul Pogba
Money is apparently no object, as Daily Mirror reporter David Maddock has credited Rodgers with a list of targets featuring Juve's star-studded duo Vidal and Pogba:
The Anfield giants have already signed Rickie Lambert, Adam Lallana, Emre Can and Lazar Markovic this off-season, but appear certain to more than DOUBLE that outlay before the window closes at the end of August.
As well as Remy, Lovren and Davies, Rodgers will also target a top class midfielder - with names such as World Cup stars Arturo Vidal and Paul Pogba on the radar.
Those are very bold plans indeed. Both Vidal and Pogba are considered among the very best at their position. They each offer physicality, energy, technical grace and scoring potential.
This isn't the first time Vidal has been linked with a move to the Premier League this summer. But Liverpool's arch-nemesis Manchester United have been most frequently mentioned so far.
However, Daily Mail reporter Simon Jones has stated new United boss Louis van Gaal doesn't favour a move for the 27-year-old Chilean ace. That creates a potential opening for Liverpool.
Vidal is a player who covers ground, creates and found the net 18 times last season, per WhoScored.com. His complete game would give Liverpool the kind of midfield general that skipper Steven Gerrard was in his prime.
With Gerrard now playing a more withdrawn role, Rodgers needs a dynamo further forward. It would certainly please Liverpool fans if their club snatched a player many United supporters would welcome with open arms.
Vidal is not for sale. He is one of the most important players in the squad. He is happy to be here. Many things have been written. We’ve never put him up for sale. Important clubs have asked after him, but we have never sat down to talk. The player decides and yesterday Vidal showed that he is happy to continue with us.
A deal for Vidal may or may not be a viable option. If it's the latter, then perhaps Pogba will do. The 21-year-old French international would rate as one of the greatest consolation prizes of all time.
Since leaving United for Turin in 2012, Pogba has become the complete midfield package. He's strong, quick and intelligent.
Pogba can mix it up in the middle as well as any classic destroyer. But he also plays with a natural flair and exuberance any stylish playmaker would be proud to possess.
Of course, those skills don't come cheap. Juve have apparently told interested clubs that £60 million will get them talking, per Daniel Taylor of The Observer.
Yet as it crazy as it sounds, that fee may not be out of Liverpool's range after receiving £75 million for Suarez, per BBC Sport. Pogba is the kind of midfield talisman who can inspire Premier League title wins rather than near misses.
Maybe a club that hasn't claimed the title in England's top flight since 1990 should consider that a good reason for a monster investment in the game's brightest young thing.
But one reason to pause on the idea of a Liverpool bid for Pogba is provided by the club's business so far this summer. Rodgers has already signed four new recruits.
That shows an approach geared as much toward quantity as quality. However, the arrival of his chosen quartet isn't enough for Rodgers.
He intends to continue spending and has made Remy one of his prime targets, per Liverpool Echo reporter James Pearce:
Those deals were all lined up prior to Luis Suarez's club record £75million move to Barcelona and owners Fenway Sports Group will allow Rodgers to use that cash to further strengthen the club's Premier League title challenge.
Liverpool are in the market for another striker and are keen on Queens Park Rangers' Loic Remy, who has a £8million release clause in his contract.
Remy fits well with the pacy attack Liverpool used to terrorise Premier League defenders last term. The Frenchman would form a feared, pitch-stretching trio with Daniel Sturridge and Raheem Sterling.
Remy can play as a centre-forward or on the left of a three-pronged attack. That should appeal to Rodgers, a manager who likes his players to be flexible enough to allow him to change formations during games (although he should note Remy is most effective through the middle).
Who Should Liverpool Sign Next?
Rodgers has already lost out to the Gunners in the sweepstakes for Chile attacker Alexis Sanchez. However, he could snatch a nice bargain in Remy to add to a forward line that remains talented even without Suarez.
The latest transfer rumours involving Liverpool certainly serve as evidence of the club's intention to be major players in this summer's market. The Suarez money has made all levels of deals possible.
But Liverpool have still lost their only elite player, the one who made the difference last season. Replacing that type of talent will require more than just buying players in bulk.
It may need at least one major deal for a marquee name.