The Rams have been linked with a loan move for Stead - who was sold by Keane at Sunderland - but the former Manchester United captain does not believe a deal is close.
He said: "No-one is close to leaving, though of course that could change very quickly.
"There have been one or two calls to the chief executive at the club.
"I've heard nothing about Jon Stead and Derby County, though it wouldn't surprise me because I left him out of the squad on Saturday. It would not surprise me if there were enquiries."
Ipswich 5/4, Watford 2/1, Draw 12/5