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The Hungary international is out of contract next summer after previously rejecting a new deal, while Celtic saw an offer worth around £2.5million knocked back during the transfer window.
Toth again demonstrated his importance with a string of outstanding saves in Tuesday's 1-0 win at Bristol City, and Mowbray revealed discussions over the 29-year-old's future remain ongoing.
"I came into the situation, really," said Mowbray.
"I get on well with Balazs. I still don't think it's a done deal that he'd be leaving.
"I know his contractual situation is what it is and it's running down. I'm pretty sure there are conversations being had and, if at any stage I can get involved to help the situation, I will.
"I was a footballer for 20 years. I've got my own thoughts that I can share with Balazs if need be. But at the same time, I fully understand football is a short career and he's got a family.
"If somebody's going to help change his life financially, then good luck to him. It's only his performances that get him a move to a place that can pay those salaries.
"With the relationship I've got with him, I can try and persuade him that this is the best place for him."
While Mowbray accepts Rovers would struggle to compete financially if a major offer arrived, he stressed there would be no resentment towards a player seeking to secure his future.
"If a club with the resources to blow this club's financial structure out of the water comes in, history tells you people move on, and good luck to footballers," he said.
"I never bad-mouth them or fall out with them because they think they can get a better move and a better deal for their families.
"Balazs is an amazing lad, an amazing guy and an amazing goalkeeper. The save where he stretched his left arm and fingered one around the post the other night was incredible, and he did it two or three times.
"Nobody's getting carried away with winning 1-0 at Bristol because, without the right goalkeeper making those saves, we could have lost 3-1 or 4-1.
"But I'm happy he's still here, working hard, doing the job and giving the impression that he's loving playing for this team and helping us win games."
Mowbray would not be drawn on the status of talks with other players whose contracts expire in 2027 - up to 13, although at least three of those have options. But he reiterated the importance of protecting the club's assets.
"That's part of every football club every day," he added.
"You have to protect your assets and look after the players. Having been a footballer myself, they have to feel content and wanted at the football club.
"They have to feel appreciated and rewarded for what they're doing on the grass."