Bowyer formed an impressive partnership with Barry Ferguson last season which ensured Blues finished ninth in their first term back in the Barclays Premier League. He lost his place during the current campaign to Craig Gardner who is currently the club's leading scorer with four goals.
But Gardner's ankle injury earned Bowyer a reprieve - and he responded by scoring the winner against Chelsea at St Andrew's last weekend.
McLeish said: "It's difficult to keep everyone happy and guys like Lee Bowyer, Kevin Phillips, Matt Derbyshire and David Murphy want to play.
"Lee knocked on my door at the beginning when Gardner took his place. It would be great in one way if the players didn't do that because you wouldn't get the hassle.
"But if you've got players who don't want to play, you're really struggling. Lee wasn't delighted at being left out but he's knuckled down, trained hard and never put a foot wrong against Chelsea. His goal was trademark Lee Bowyer, coming from the sort of runs he has been making all his career."