However, McLeish concedes the club are unlikely to be able to afford a player such as Wheater, but he does like him.
He also revealed Luccin's recent cruciate ligament injury has seen his chances of a move to the Premier League new boys scuppered.
Many Blues fans feel a big defender is needed and McLeish was quizzed about the likes of Steven Taylor and David Wheater - should Newcastle and Middlesbrough be relegated.
"With all due respect, who are we going to be able to buy to satisfy our supporters, totally?" said McLeish at a local fans' forum.
"It's difficult for us to buy top-end centre-halves in the Premier League.
"If Middlesbrough go down, then Wheater? He is a decent player and someone we have watched over the last five weeks just in case they say 'do you want a bargain'?
"But we think they will be looking for about eight or nine million pounds."
When asked whether the club had eight or nine million, he replied: "Not for one player.
"Listen, I don't think it's the time [here] for me to say 'the directors have got to give me 30 or 40 million'.
"I would love to be given that kind of money.
"But what you have to understand and respect is that if you look at Sunderland who, okay, it seems as if they might survive, but they are in the mix to go down and they have spent £90m over two years.
"Now that's scary for a lot of owners of clubs.
"I had a conversation with David Sullivan and said 'why don't you give me 30 or 40 million'? and when he explained all these things and you listen to the board telling you these things, it's difficult to have an argument against them.
"So I said I will do my very best to keep us in the Premier League with the resources we have got.
"It's up to us to find the right players and to coach and educate the right team to be able to stay in the Premier League and make us hard to beat, like Stoke," McLeish added.
"And I think if you look at them, they've spent a right few quid [£27m], and they are a very difficult team to play against.
"I'd love to give you an entertaining Arsenal, Man United team, one like that. I will definitely strive to get the quality in.
"But I have got to make us hard to beat. We can't go to Villa
Park and be as open as we were in my debut season, for example.
"And £9million for Wheater, it would be difficult for us to pay that."
McLeish revealed his disappointment at not being able to bring in Luccin, who was injured whilst playing for Racing Santander in Spain.
"We had a player lined up in Spain we've watched over the last few weeks. Unfortunately he's just done his cruciate," he said.
"It was Peter Luccin. I know Birmingham have looked at him before. He's excellent on the ball and a player of that ilk, that quality, is what the team needs."