Manager Neil Lennon today confirmed his club had turned down the bid after reports emerged in England.
Lennon said: "The bid has been rejected. We had discussions with his representatives this morning and we are waiting to hear back from them."
Celtic have been attempting to persuade the English striker to extend his contract, which expires at the end of next season.
Lennon, whose team face Juventus in the last 16 of the Champions League next month, said: "We are in a good position. We don't want to sell, we feel we have a lot to look forward to in the second half of the season.
"We don't want any of our top players to go and Gary comes into that bracket."
Lennon added: "I've not spoken to him because I was with his representatives most of the morning. I'm sure they'll have a discussion later on.
"Our case is simple - you are not going. He has a year and a half on his contract and he's a Celtic player."
"The talks were positive and we made our position pretty clear. We left his representatives to it. They will go away and digest it and come back to us."
Essex-born Hooper has scored 68 goals in 114 games since joining Celtic in July 2010 and has been tipped for England honours after helping the club into the knockout stages of Europe's elite competition with two well taken goals against Spartak Moscow.
And Lennon revealed Celtic were not minded to cash in on the 24-year-old, who they bought from Scunthorpe for £2million, despite their failure to tie him down for longer.
"I haven't come to that point yet," he said. "(In the summer) he will only have a year left and he may want to run down his contract. I've not spoken to him about future scenarios.
"For the time being, we have rejected the deal, I'm annoyed it has come out publicly. I'm annoyed with people down the road letting it come out publicly.
"I can't point any fingers but it has certainly not come out from this end."
Lennon added that he was "pretty confident" Hooper would be at the club when the transfer window shut.
"It's like everyone else - they all have their price," Lennon added.
"But when a transfer comes in way under our valuation then the club is quite right to say no."
Lennon has added two players to his squad this month, although a deal for 20-year-old Australia midfielder Tomas Rogic depends on a work permit hearing on Monday.
Israeli defender Rami Gershon, who has joined on loan from Standard Liege, could make his debut against Hearts tomorrow.
Lennon said: "Tomas is an excellent talent. He is young but has developed very, very well over the last year.
"He is a good mover of the ball, he has got a goal in him and technically he is very good.
"Rami is strong, aggressive, hungry and we think they will both be good assets."
Celtic face a Hearts team missing the suspended Marius Zaliukas and Ryan Stevenson but Lennon is demanding focus from his side as they return from the winter break.
Celtic have cup ties against St Mirren and Raith Rovers to come before they face Juventus and Lennon wants to make sure they are firing on all cylinders.
"We`ve got a big week with Dundee United on Tuesday and the semi-final on the Sunday," he said.
"John (McGlynn) has a few injuries and suspensions and players leaving.
"He has mounting problems but Celtic-Hearts is always a decent game and they made life very hard for us in the fixture early in the season."
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