As revealed by The Mail, Molyneux is the subject of significant interest as the 24-year-old nears the end of his contract at the Suit Direct Stadium.
And while Lee has acknowledged that interest, he has suggested they are doing everything they can to retain his services.
“We’re doing whatever we can and we’ve been fighting to do whatever we can,” Lee told The Mail.
“But you know it’s a difficult situation regarding a player who might have interest elsewhere because of his performances in the cups and different things against higher league opposition.
“He has shown that he can play against teams from them leagues.
“I think he’s got interest, but we’re fighting to see what we can do to keep him.”
Molyneux went off with a potentially serious injury in Tuesday’s draw with Mansfield Town, although Lee believes it is better than originally feared.
But with Molyneux on the sidelines for the immediate future, it could be an opportunity for Pools to try and push through a deal with the former Sunderland striker.
“It’s a nice opportunity to get some clear answers with what we want to do,” said Lee.
“Luke’s 24-years-old. As much as we wished him happy birthday I wish it wasn’t his birthday because he comes out of contract and he’s available to speak to other clubs.”
Molyneux has made 50 appearances this season scoring 12 goals but is out of contract in the summer meaning he is free to negotiate with other clubs.