The Blackpool midfielder is out of contract at the end of next season and is available for around £4million.
On the radar: Charlie Adam is wanted by a host of clubs in the Barclays Premier League
Aston Villa have already failed with a £2.5m bid, while rivals Birmingham are also in the hunt.
However, they could now both be pipped by Liverpool, who want to take the Scotland international to Anfield.
Dalglish is not expected to make wholesale changes in the January transfer window but he still feels the squad requires additions.
Adam should line up against Liverpool at Bloomfield Road on Wednesday night in what could be his final appearance for Blackpool.
Tough job: Kenny Dalglish (right) is weighing up targets with director of football Damien Comolli
He has played a key role in their impressive debut season in the Barclays Premier League as they attempt to avoid an instant return to the Championship.
Although Liverpool have reservations about whether he is the right man to revive their season, they may be willing to gamble on his signature.
Adam ran the show at Anfield earlier this season when Blackpool secured a shock 2-1 victory. He scored a penalty in the win.
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Explore more:People: Kenny Dalglish, Charlie Adam Places: Birmingham, Liverpool, Scotland