Best is being linked with a Premiership move, with Wolves keen.
Coventry have offered the 23-year-old an extension, but manager Coleman concedes the club may not be able to match the Republic of Ireland international's demands.
"The chairman has talked with Leon's agent and, as always, they want one thing and we want to give another," Coleman told the Coventry Evening Telegraph.
"We have been talking for some while because we are very aware that his contract runs out in the summer, but we can't give what we haven't got. We think we can offer him a good contract, but ultimately it will be up to Leon to see what he wants to do.
"We want to keep him and we have said that all along."
Wolves have been linked with a £1.5million January bid for Best, but Coleman says there have been no approaches for the former Southampton youngster.
He added: "I have seen one or two stories about other clubs expressing an interest, but we have not received one bid and I have not had one call. All I care about is whether he is playing well and scoring goals, and if he does that and if we can give him a contract that keeps him happy and keeps him here, brilliant - that's obviously what we want to do.
"There will always be Premier League clubs sniffing round if you have got a player doing well. You have just got to get the best deal you can because it is a rare case where a player says they don't want to go from this league to a big Premier club for a lot of money."