The Scotland international is out of contract in the summer and Blackburn Rovers and Bournemouth are believed to be keen.
This morning it was reported by the Scottish Sun that two English clubs were keeping tabs on a Celtic star for the summer.
Charlie Mulgrew is out of contract at Celtic in the summer and the report claimed that negotiations over an extension have not yet begun. With that in mind Blackburn Rovers and Bournemouth are said to be keeping tabs on his position ahead of a potential move beyond the border.
Mulgrew, who can play in both defence and in midfield, has been suffering with a thigh injury all season which has seen his play time limited. With that in mind Celtic have held off on contract talks.
Discussing the future of Mulgrew in his Celtic press conference today manager Ronny Deila admitted he was not surprised to see teams interested in the Scotland international:
"It's normal a player of Charlie's standard that other clubs are looking at him.
"He has only played a one game in a long time so his and our focus is to get him up to his best level."
Mulgrew joined Celtic in 2010 from Aberdeen and has previously played in England with Wolverhampton Wanderers.
The 29-year-old, who turns 30 next month, might be at his last chance to move to an English club and with his contract expiring now would be the best opportunity.