The 24-year-old signed a five-year deal with the Scottish Premiership leaders earlier in the season.
Dudu Dahan had reportedly stated that a handful of offers had been made for the 24-year-old, but the Record has claimed that even if there had been bids for the Israel international, the Hoops were not prepared to let him go.
Bitton signed a new five-year deal with the club earlier on in the season (via Record), and has been a key reason why the club are closing in on their fifth consecutive Scottish Premiership title.
Despite often being used in a holding role, the former Ashdod man has scored eight goals in all competitions for the Bhoys, including five in the league, and has also contributed four assists in the top flight.
Perhaps his best moment of the season came during Celtic's trip to Rugby Park to face Kilmarnock in August when he found the top corner from around 35 yards out to give his side a 2-1 lead in a game they would ultimately draw.
It is moments like that that have persuaded the club to put so much faith in him by handing him a long-term deal, and why the Record suggest that he is now valued at £10m.
And with Celtic reportedly set to dig their heels in regarding his future, it appears that it may take a figure much higher than that to tempt them into even considering a deal.