Harper was handed his Celtic debut in Monday night’s 1-1 draw with Hibernian and the Bhoys have been looking to lock him down on a new contract.
The forward is out of contract at Celtic Park in the summer and the Scottish champions have put a deal on the table.
MLS side New York Red Bulls though are confident that they will be able to sign Harper on a pre-contractual agreement and he will snub Celtic.
Harper is claimed to have wanted to be assured over the level of his involvement in the first team at the Bhoys.
Red Bulls are confident that they will sign Harper and it is claimed they have not ruled out being able to bring him into the building before the new MLS season kicks off.
A move to New York would see Harper head back to his native United States.
He could depart Celtic having only made one senior appearance for the club.
