Derek Riordan's agent has told BBC Scotland the striker wants Celtic to sell him before the end of the January transfer window.
Riordan has made just 10 appearances for Celtic this season
Riordan, 23, has become frustrated at the lack of first-team football and was the subject of a failed bid by Burnley earlier this week.
The Championship club's £400,000 offer fell short of Celtic's valuation.
"Five clubs want Derek on loan, but if he's to go it must be on a permanent basis," agent Jim McArthur said.
Riordan, who signed from Hibernian in 2006, has made just 10 appearances for Gordon Strachan's side this season.
McArthur said the striker wanted to move, adding: "I'm sure it would suit all parties if an agreement could be reached.
"The only club to have made an official offer is Burnley for £400,000 plus add-ons.
"Derek would be very keen to speak with them if an agreement was reached."
Strachan has said he is not looking to sell any of his squad during the transfer window.