The 23-year-old full-back - who is out of contract this summer - has turned in a series of impressive performances in League One this season, causing his agent, Jonathan Hope, to tip his client for a move to a bigger club.
"I am currently exploring options for Danny," he told skysports.com. "Tranmere Rovers wouldn't stand in his way to step up a level to improve his career as he has been having an absolute cracking season and thanks has to go to them for that.
"I had a call from Glasgow Celtic in regards to Danny's availability and Liverpool have not ruled out a move for the youngster."
Reds boss Kenny Dalglish is known to be in the market for bright young talent, and Holmes fits the bill in terms of prospective targets that Liverpool director of football Damien Comolli wants to lure to Anfield.
However, the club may miss out on the opportunity to land him without the guarantee of regular first-team football, putting Celtic manager Neil Lennon in the driving seat when it comes to negotiations over a potential move to Parkhead.
"I have to be realistic and put Danny at the right level so he is guaranteed game time," Hope continued. "There is no point in putting him up in the Premier League when he is still developing.
"Danny Holmes will eventually play in the Premier League, as he is developing at a very fast rate through true professionalism. He has supported Tranmere all his life but I don't believe the fans would complain about a boy furthering his career."