The 25-year-old appeared to be heading for the Keepmoat Stadium exit door following Doncaster's acceptance of a bid from Leicester last weekend.
However, Saunders has now confirmed that Sharp is likely to remain with Rovers until the end of the season.
"As far as I know Billy will be staying with us until the end of the season. That's a great boost for everybody," he said.
"If he can win us six or seven games between now and the end of the season it's worth millions to the club. And if he gets six or seven winners he'll probably be worth £3.5million and have Premier League clubs looking at him.
"We've tried everything to make him stay and I'm pleased he is staying. He's indicated to me he's not going to Leicester but somebody else might come knocking."
Sharp has scored ten league goals this season.