The striker was close to a move to Ewood Park after reports suggested the player was undergoing a medical at Blackburn.
Despite a reported £2m bid from Rovers, the Scottish champions have refused to drop out of the race to sign the Dundee United frontman.
"Unfortunately I can't give you a lot of information, other than we have put in a new bid to Dundee United,” McCoist told Sky Sports. "We just have to wait and see in the next couple of hours what happens.
"We've all made no secret of the fact that David is a player we would love to see at Rangers. We believe that we have put a bid in that's more than acceptable."
Blackburn are said to be offering £800,000 in add-ons as well as a sell-in clause for the striker.