The Heisman Trophy winner met with the media Friday in the lead up to the BCS championship game against No. 2 Auburn.
He says he and his teammates have not concerned themselves with the speculation and reports about Fisher being a candidate to replace Mack Brown at Texas.
He added, jokingly: "Even if Coach Fisher goes to Texas, I'm going to ask him can I go with you? Yeah, I'm serious. He's my coach."
Fisher chuckled when heard about Winston's joke.
"He and I have a tremendous relationship," Fisher said. "I think the world of him. He and I are very close, but we'll be right here."
Fisher said he has not heard from Texas, but knows his name will remain in the rumor mill.
"It doesn't matter what I say, y'all are going to write what the heck you want until someone takes that job," Fisher said with a laugh. "So, we're not going down that road. We're going to worry about a national championship right here. That's what I'm focused on and happy about."