The Daily Mail reports that Dalglish has long followed the 28-year-old and could make a move this summer.
Dalglish plan to bring in around six signing this summer and players such as Blackburn’s Phil Jones, Blackpool’s Charlie Adam, Aston Villa’s Ashley Young and Stewart Downing and Ipswich’s Connor Wickham are among the players the Reds are being linked with.
Barton has 12 months left on his current contract at Newcastle.
