The 22-year-old has been linked with several Premier League clubs in recent months.
“David Wheater is exactly what this club wants. He’s totally committed to this club, he is as great lad and if you ask him to do something, he will do it. He is Middlesbrough through and through,” Gibson said.
“I think there’s more to come from David. Fabio Capello included him in his England squad not that long ago. Since then, he’s experienced a lot of change that hasn’t helped him.
“Ultimately, I have an influence, but I don’t pick the squad, Gordon Strachan does. But Gordon loves him.
“David’s conduct around the place doesn’t suggest he wants to go and he’s not the kind of lad or player that we would want to leave this club.
“I want David Wheater at Middlesbrough Football Club.”