Bowyer played a key role in tandem with Barry Ferguson in steering Blues to a top-10 finish in the Barclays Premier League last season.
But he was axed for the opening home league game of the campaign against Blackburn, with McLeish preferring Craig Gardner who justified his call-up with two goals.
Since then Bowyer has had to play mainly out of position on the left flank, with Gardner given the more central role and licence to go forward.
But the 33-year-old could be back in the middle for the home clash with Everton as Gardner starts a three-game ban for his red card against Wigan.
McLeish said: "I don't want a player who is happy when he is dropped and Lee is a proud guy. He played a major role last season in the middle with Barry Ferguson. They formed a great partnership.
"It really was a risk taking a player like Lee out of the team last season. He got six goals last season. On that day I was proved right with Gardner coming in and scoring two goals.
"It didn't mean that Lee wouldn't have scored two goals - we'll never know that - and it's my right to chop and change the team.
"But I have certainly got no doubts about Lee's ability and what he brings to this side when selected. Bow is 33 but he's got great legs, he runs for fun and he's still got a great engine.
"There's no red mist or rush of blood as there was in yesteryear, he's pretty mature now."
Source: PA
Source: PA
Source: PA