The Sky Blues boss has revealed a second bid from an unnamed club has been rejected, with Nottingham Forest believed to be the suitors involved.
It is understood Reds boss Billy Davies has now also made a third attempt to sign Fox, but that none of the offers have been above £2million.
Coleman, who labelled the first offer received as "pathetic", told the Coventry Telegraph: "One club has made two offers for Fox but they are well below the valuation of a player who was voted the best left-back in the Championship last season.
"We do not want to lose him or sell him but this is the state of football at the moment."
Meanwhile, Clinton Morrison's first-half header from a David Bell corner handed Coventry a 1-0 victory over Nuneaton Town in the club's second pre-season outing on Wednesday night.