Last month, Wheater reiterated his intention to honour his contract that expires at the end of next season, insisting that he will not agitate for a move if Boro fail to secure promotion this year.
Strachan is determined not to become embroiled in a repeat of the scenario that saw Adam Johnson snatched from under the club's nose midway through the final year of his Boro deal and will ask Wheater to commit his future to the club.
The £8m raised by Johnson's sale to Manchester City helped fund Strachan's recruitment of the likes of Scott McDonald and Barry Robson, but the manager regards Wheater as an integral part of his long-term plans and will fight any attempt to lure the academy product away from his home turf.
If Boro can find a way back to the Premier League via the play-offs they will be in a much stronger position to persuade Wheater his future lies on Teesside. Defeat in the 5.15pm kick-off at The Hawthorns this afternoon, however, would effectively end their slim hopes of making an immediate return to the top flight.
We will do everything that anybody could do to keep David here, confirmed Strachan.
I'd rather get it sorted out right away, rather than have the situation we've endured this year, where we've had six or seven contracts up. But I can understand that, with the club not really knowing where they are going financially.
Emanuel Pogatetz, Jeremie Aliadiere and Chris Riggott are among the players whose deals expire this summer.
I like working with David and there is a lot more to develop with him,'' he said.
I like having him in my team and having him about the place. He is a good influence.
We are seeing him back to form now, which is good.
But, like everything else, it is a financial decision.
I love these quotes where I read players saying they don't really want me that much', when what they are really saying is the club aren't offering me what I want.' They measure how much they are loved in pound notes.
I've seen it happen at clubs where players are unhappy because they are offered £80,000 per week and they wanted £100,000.
But David has a fantastic affinity for Middlesbrough.
We'd like to see him here.
Wheater's return to form has been one of the key factors behind Boro becoming far more resolute than the side trounced 5-0 when West Brom visited the Riverside last September.
They have conceded only eight goals in their last ten matches but their defensive solidity will be tested thoroughly this afternoon against the Baggies, who will be looking to celebrate their promotion in style.
The manager hopes to pair Wheater with Stephen Mc- Manus next season if a permanent deal can be agreed for the on-loan Celtic defender.
While Wheater and Mc- Manus have become mainstays of the side, Strachan revealed that none of his strikers have staked a claim to be regarded as automatic selections.
What has been good is that teams now find us really hard to beat, touch wood. That is a basis you can work from,'' he insisted.
I have said that consistency comes from a settled back four. The only change we've had in the last few games is at left back.
But I never said you had to be consistent in your selections up front. It's nice that you can chop and change and I sometimes play a quicker striker against people I think are slow, or I put guys up front to hold the ball up or are good in the air.
If somebody is playing that well then we shouldn't worry about it because they pick themselves. But I don't think I have a (strike) partnership that have picked themselves.
Scott (McDonald) is not an automatic choice if he is fit. It is not fair on the rest of them.