Yeung, who is now in full control at City after an £81.5million takeover, has given his full backing to McLeish in the battle to establish the club in the top flight.
He has shown his faith in McLeish by pledging to make up to £40million available for new players in January.
But McLeish, who revealed he is on a rolling contract, is not thinking about his own future and has the same ambitions of the Hong Kong businessman.
McLeish said: "I have a rolling contract but a new contract is the furthest thing in my mind to be honest.
"I've got my head down here at Birmingham City since the day I arrived about two years ago and it's been really about staying in that league.
"We couldn't do it at the end of my first six months here but we came back up the first time.
"Again we can talk about all these things if that (survival) is achieved. But I'm not interested. It's not about money for me.
"It's about ambition, it's about winning, it's about getting these players to get tougher and stronger mentalities to help them become better players."