League One outfit Leeds United currently head the queue for the Northern Ireland international after making an enquiry earlier this month.
Baxter insists there are no bids on the table for the 23-year-old stopper, who he is unwilling to put a price on anyway.
As Coates has two years left on his Crusaders deal, Baxter insists that unless 'big money' is offered his prized defender will be going nowhere.
"Colin has a two-year contract, so unless someone comes in and puts big money down, he will be staying with us," he told the Belfast Telegraph.
"No-one has put a shilling down and I would definitely not put a figure on a player's head.
"The speculation about Colin was inevitable after his international call-up, but it is good for us as he knows the stakes are high and to attract other clubs he needs to be playing his best football."