The attack-minded left-back, 23, has been heavily linked with a move to West Brom, speculation that has only intensified following Paul Robinson's loan switch to Bolton.
Baggies boss Roberto Di Matteo last week denied his interest in Fox, but several other clubs have also been linked, including Nottingham Forest.
Coleman, while admitting a "massive bid" could change matters, told the Coventry Telegraph: "I have got to be honest with our supporters and I can't stand here and say that we are not going to lose any of our players, but we don't want to sell anyone.
"I'm not surprised by the interest in Danny. He was voted in the Championship team of the season and he deserved that along with Keiren Westwood, and he has come back and looks even better than last year. He is in top form and his quality in training is absolutely fantastic.
"I have had one conversation with one club about Danny Fox. There was a bid that I thought was pathetic for a player of his calibre and we said no. I told Danny that and he's fine, he's happy where he is so that's where we are at."