The Merseyside club are scheduled to hold a news conference on Friday at which they are expected to present Northern Irishman Rodgers as the successor to Kenny Dalglish.
"Both clubs have been in discussions to sort suitable compensation for Brendan along with assistant manager Colin Pascoe, performance analyst Chris Davies and head of sports science and medicine Glen Driscoll," Swansea said on their website.
"The club now starts its search for Brendan's successor."
Swansea announced on Wednesday that Rodgers, 39, had been offered the Liverpool job subject to compensation being agreed with the Welsh club for their highly regarded manager.
He turned down an offer to talk to Liverpool earlier this month and the Merseyside club's American owners then held discussions with Wigan Athletic manager Roberto Martinez.
Rodgers guided Swansea to a respectable 11th place finish in the Premier League last season, their first campaign at the highest level since 1983.
He led the club to promotion from the Championship via the play-offs after moving to Swansea in 2010 following spells in charge of Watford and Reading.
WORST FINISH
Liverpool have been searching for a replacement for Dalglish, whose second spell in charge at Anfield ended when he was dismissed after the club ended the season in eighth place, their worst finish for almost 20 years.
Dalglish did steer Liverpool to a League Cup triumph and an FA Cup final appearance last season but the club are desperate to get back into the top four and mount a title challenge.
Once the dominant force in English football, Liverpool have not won the championship since 1990.
They finished the 2011/12 campaign 37 points behind champions Manchester City and recorded their fewest wins (14) in a top flight season since 1953/54.
Swansea have been given permission to talk to Wigan's assistant manager Graeme Jones after making a formal approach to the club, Athletic's chairman Dave Whelan said on Thursday.
"We don't want to lose the lad, he's a good lad," Whelan was quoted as saying by the BBC. "But you can't stand in their way if they want to progress, and we got him from Swansea so it's only fair we let Swansea speak to him if they want to."
