After QPR joined Norwich City and Hull City in the race to sign the English striker on Monday, Bhoys assistant manager John Mjallby admits that a sale is now "likely"
The 25-year-old is a man in demand after scoring 31 goals in all competitions last term, with the two Premier League clubs having already had close-season bids rejected.
QPR also joined the chase on Monday but saw their initial offer turned down by the Scottish Premier League champions, though Mjallby still expects the forward to eventually be sold.
|5/2||Celtic are 5/2 with PaddyPower to win 10 SPL titles in a row
"They increased the bid a wee bit when it came in. If it is good enough, I don't know. That's something you have to ask the chief executive, the manager and the board.
"We know it looks likely right now that Gary is going to leave the club. I'm not too sure the final word has been said yet. We have to wait and see.
"I think the club is going to sit down and think about it. If he has played his last game, I don't know."
Hooper did not fly with Celtic to Belfast ahead of their Champions League qualifier against Cliftonville on Wednesday, with Mjallby claiming that the striker has a groin strain.
The Bhoys have already sold midfielder Victor Wanyama to Southampton this summer.