Fenway Sports Group, Liverpool's owner, expect to announce the club's new manager by Friday having reduced their search to a shortlist headed by Rodgers and Wigan Athletic's Roberto Martínez. No formal approach has been made to Swansea for Rodgers, who rejected Liverpool's offer of an interview two days after Dalglish's dismissal, but FSG have earmarked the 39-year-old as their preferred choice and are confident Rodgers will reciprocate their interest when he receives an offer of the job.
They also believe obstacles complicating a move to Anfield, such as compensation, Swansea's reluctance to lose their manager and the new management structure intended for Liverpool, can be overcome in the next few days.
Rodgers signed a new three-and-a-half-year contract with Swansea only in January that includes a release clause of around £5m. He later admitted, amid reported interest from Tottenham Hotspur at a time when Harry Redknapp was favourite for the England job, that it would require an agreement with the Swansea chairman, Huw Jenkins, to activate the clause.
"I didn't put any clause in my contract to say if a top-four club comes in then I can speak to them. Not at all," Rodgers said. "The only item that was in the contract was if a big club came in and wanted me, and the chairman and I felt it was right for us to move on, then I wanted the club to benefit from it. That was very important for me that if I left the club would get rewarded. Other than that, I didn't want to instigate anything in the contract because I wanted to show I was happy here and continue to work."
Swansea would be loth to lose the manager who guided them to promotion to the Premier League followed by an 11th-place finish in the top flight last season. On Monday Jenkins dismissed as "pure speculation" reports of talks having been arranged between Liverpool and Rodgers and has announced a club record £6.8m deal with Hoffenheim for Gylfi Sigurdsson, the Iceland midfielder who made a stunning impact on loan at Swansea last season. That transfer, due to be finalised at the end of the week, represents a major statement of intent from the Welsh club under Rodgers.
The Swansea manager held talks with Jenkins on Tuesday following his return from a holiday in the United States. The club claim it was a prearranged meeting to discuss the Sigurdsson signing and possibly that of Tottenham's Giovani dos Santos, who Rodgers watched during Sunday's friendly between Mexico and Wales at the MetLife Stadium in New Jersey, where he was a guest of the Football Association of Wales. But Rodgers was aware of Liverpool's interest prior to his meeting with Jenkins and the size of his release clause would not deter FSG.
Martínez also returned to Britain from a family holiday on Tuesday but has not yet held a second round of talks with Liverpool's owners, as predicted by the Wigan chairman, Dave Whelan. They are likely to take place on Wednesday. Martínez met Liverpool's principal owner, John W Henry, in Miami last week and has been given until Thursday by Whelan to decide on his future amid renewed interest from Aston Villa.
The Spaniard's proposed move to Liverpool is complicated by FSG's intention of appointing a sporting director-type figure at the head of a new management structure. Louis van Gaal is a leading candidate for that role but the Dutchman may wish to be considered for the manager's position, a stance that is at odds with FSG's vision.
Meanwhile, Mohamed Diame, Martínez's former midfielder at Wigan, has revealed he was set on a free transfer to Liverpool until Dalglish was sacked as manager. The Senegal international, who is out of contract this summer, said: "I met Kenny Dalglish and we talked about next season but God decided to finish this situation. It is true. I was very sad in my head as I was thinking to go there but that is okay as I think I have got other opportunities to go to another club. I have got some offers from Spain, from France, from Turkey, but I really want to stay in the Premier League."