McLeish says he overcame failing to secure a move to Manchester United as a player and would expect the same response from Downing if he is still at Villa next season.
He said: "I've spoken to Stewart, I've told him I don't want to sell him.
"There's an obvious distraction there for him but he's been a credit to himself and applied himself in the right way and worked his socks off in training. I don't see a problem professionally.
"That was a big disappointment but I got my head down and worked and I don't doubt Stewart has the character to get through this is he stays at the club.
"It's part of your growing up as a footballer."