Steele has caught the eye of Premier League scouts since breaking into the first team at the start of the season, and weekend reports linked Arsenal with a possible £4m bid for the goalkeeper.
The Newton Aycliffe-born 20-year-old is out of contract at the end of next season, and an early round of contract talks has so far failed to result in a new deal.
Mowbray is expected to sell a number of players as he attempts to alter the make-up of his squad during the January transfer window, but Steele will not be allowed to pass through the Riverside exit door no matter what offers are made for him.
I can't see any reason why we would need to sell a young goalkeeper who is just starting his career, said the Boro boss. I don't think there's any danger that would happen.
I would like to think that we can work with Jason for the next few years, if not beyond, and help him develop. In particular with goalkeepers, I think they should be playing games.
Sometimes, the lure of a so-called big club doesn't actually help the development of their career. They can find themselves sitting in the reserves, not playing much football, and their development is stifled.
I am confident we will have no problems with Jason Steele, and somewhere down the line we'll hopefully be extending his contract and settling him down to continue to play for us for a lengthy spell.
However, changes are likely at the turn of the year, with Boro's finances, and the increasing likelihood of a third season in the Championship, necessitating a reduction of a wage bill that remains one of the highest outside the topflight.
Mowbray will be able to reinvest some of the money he raises, but until he receives firm offers for his players, he admits it is hard to start targeting potential recruits.
It's not really a case of identifying areas we'd like to improve, he said. There are going to be some holes created in our squad that will need filling.
I don't think we're in a position to start building for the long term yet, we need to reduce and then start to build and fill from there.
I'm not sitting here thinking, Right, we're off to get a centre-forward or any given position' because there needs to be a hole created before we can spend to do that.
Indeed, while Mowbray had previously expressed a desire to bring back all of Middlesbrough's loan players, the former skipper has conceded the size of the club's wage bill could yet result in Andrew Taylor or Jonathan Grounds staying out on loan for the second half of the season.
The defenders are currently at Watford and Hibernian respectively until January, and with Joe Bennett having impressed at left-back in recent weeks, Mowbray could be tempted to keep at least one of them away from Teesside.
I don't really have to assess either situation at the moment,
he said. But there are financial implications to think about and I'll be assessing things in due course.
There's a fair chance one or both could still come back, but they're both left-footed defenders and in my mind I have a pretty good left-footed defender playing in the team at the moment.
Do I want to load more outgoings on to the expenses we have already I have to give some thought on what's best for the squad and the team.
Gary O'Neil and Kevin Thomson returned to training yesterday, but the duo are unlikely to be involved in tomorrow's Championship game at Coventry City.