Rodgers sees the 26-year-old as surplus to requirements at Anfield following the arrival of Joe Allen from Swansea City on Friday and the impressive form of Jonjo Shelvey.
Rodgers and the club’s American owners want USA striker Dempsey but have been unable to agree a deal with Fulham, who value him at £10million.
But Liverpool hope the inclusion of Adam as part of the package will help push the move forward. Fulham are looking for a creative midfielder following the departure of Danny Murphy.
Rodgers is an admirer of Adam but has been surprised by the emergence of youngster Shelvey, who was picked ahead of his Scottish rival for the Europa League win against Gomel last week.
Rodgers has already begun breaking up Dalglish’s squad by letting Craig Bellamy, Maxi Rodriguez, Dirk Kuyt and Alberto Aquilani leave but he needs more departures to bring in more signings, following the arrivals of Fabio Borini and Allen.
Daniel Agger is the subject of interest from Manchester City, while Liverpool hope to agree a deal which would see £35m Carroll return to Newcastle only 18 months after he joined.
Both the Telegraph and Guardian also report that Rodgers remains keen to add width to his side, with Adam Johnson his preferred target. The England international has struggled to hold down a regular place in the Manchester City first team and could well be available this summer.
Although left-footed Johnson has established himself on the right flank and could potentially be a replacement for the departed Dirk Kuyt.
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Liverpool continued their pre-season preparations with a 2-1 defeat against Italian side Roma in front of a packed crowd at the historic Fenway Park in Boston.
Liverpool travelled to the Hawthorns on the back of a great midweek win at Stoke in the Carling Cup, but Liverpool were hoping to get back to winning ways in the League after two draws in their last two league matches. West Brom were going into the match with some decent form too and on the back of a great win over their local rivals last weekend. Liverpool lost at the Hawthorns in this fixture last season soon after former Liverpool manager Roy Hodgson had taken charge, so Liverpool were hoping for a better result this time around as they try to keep in touch of a top four place.
Liverpool will head to Glasgow in a midweek friendly later this month to take part in a friendly game against Rangers.
In the morning press, it reported that Liverpool and England midfielder Joe Cole could move to Aston Villa.
The former Blackpool man put pen to paper on his new contract on Thursday afternoon after successfully completing a medical.
Adam silenced the Kop last season by netting a penalty at the Kop end during Blackpool's shock 2-1 Anfield victory - but now he's looking forward to instead putting smiles on the faces of Liverpool fans.
Liverpool Football Club today announced they have reached agreement with Blackpool for the transfer of Charlie Adam.
After Stephen Darby and Jonjo Shelvey were proposed as two of the possible makeweights, 19-year-old Wilson is the third young Red to be linked with a move to Bloomfield Road as part of the package for Adam.
Oyston revealed 11 days ago that he had held initial talks with the Anfield club, saying in The Gazette: "We've had a few very preliminary discussions and enquiries but nothing of any substance."
Meireles, 28, eventually enjoyed a successful first season in the premier league after a slow start. Helping Dalglish’s men gain a credible Premiership spot after a troubled spell under Roy Hodgson.
The 30-year-old started his career at Newell's before leaving for Espanyol in 2002.
