Boro boss Gordon Strachan, who paid £100,000 to Livingston for winger Andy Halliday, has made just one addition to his squad amid moves for other targets.
But having lost defenders Emanuel Pogatetz and Chris Riggott ahead of next season, Strachan is not willing to raise his transfer pot by selling centre-back Wheater.
The 22-year-old only has a year remaining on his contract and talks over an extension have not even started yet.
But Gibson has responded to suggestions that Sunderland and Aston Villa are considering a move to try to tempt a sale by insisting the £6m-rated defender will be staying put.
David Wheater is exactly what this club wants, said Gibson. He is totally committed to this club, he is a great lad and if you ask him to do something he'll do it. He is Middlesbrough through and through.
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. 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'd want to leave this club. I want David Wheater at Middlesbrough Football Club.
Middlesbrough are keen to remove Mido and Didier Digard from their Championship wage bill before preseason training on June 28.
There has been a lack of interest in both players, given their Premier League pay packets.
Scunthorpe's £2.5m striker Gary Hooper, who Middlesbrough remain confident of landing despite interest from Leeds, looks destined to be one of the most expensive recruits.
Rochdale centre-back Craig Dawson remains on the radar, and it was reported yesterday the defender is demanding a transfer.
But Boro are also looking at seven-figure fees for Stephen McManus, Andrew Driver and Craig Conway. Gibson, working on a number of deals, insists Sheffield United's new signing Leon Britton was never at the top of any list.
Britton is believed to have signed a contract of around £15,000-a-week at Bramall Lane, after allowing his contract at Swansea to expire.
The midfielder has, briefly, been under Boro's consideration, but Gibson said: I am angry and hugely disappointed to read reports suggesting we lost out in trying to sign Leon Britton. That's simply untrue. Britton was never one of our main targets. He was simply a player who had been pushed by his agent. He is absolutely no loss to us.
We received an unsolicited proposal from his agent some weeks ago, which we dismissed out of hand as the figures were well beyond any valuation we might have placed on the player.
Reports making out that he was one of our main targets and that we have therefore somehow lost out on him amount to lazy journalism designed to sell newspapers.
Strachan remains interested in Scotland striker Kris Boyd, although the out of contract striker is mulling over his options.
Source: Northern Echo
Source: Northern Echo