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.
- Premier League fixtures / Premier League table
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.
- We're in relegation battle - Moyes
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."
Keith Fahey will be in contention for a recall after not starting a league game since the opening day of the campaign at Sunderland.
Meanwhile, Everton boss David Moyes believes his team are involved in a relegation battle.
The Merseysiders are bottom of the Barclays Premier League after failing to win any of their opening six games.
Few expect them to remain in the lower reaches of the table for long but Moyes is not afraid to use stark terminology.
The Scot said: "If you are in the bottom three you are in a relegation battle, whether it is after two games of the season or 32.
"It is still the same. If you are in the bottom three you have got to get out of it.
"It is a position - I don't know if you can call it false - and it is there staring us in the face.
"You take it and try to move away from it."
Aside from a 1-0 loss to Newcastle a fortnight ago, Moyes has been happy with performances.
He feels his side deserve much more than the three points they have collected but concedes two main factors are hindering them - isolated errors and, chiefly, a lack of goals.
The Toffees have scored just four times in the league - three in one game against Manchester United - with none coming from out-and-out strikers.
Of his regular forwards, Louis Saha has been out injured, Ayegbeni Yakubu is finding his way back to form and fitness and summer signing Jermaine Beckford is still adjusting to the top flight.
Moyes said: "Goals always change games. If you score and you win people don't talk about performance.
"What we have not done is score the goals to change the games.
"There have been one or two mistakes which have led to the opposition winning.
"We need to score a few more goals and keep a few more clean sheets.
"Teams can score very good goals against you and there is nothing you can do about that, but certainly the goals against Wolves and Blackburn were self-inflicted."
Moyes is hoping Yakubu, an £11.25million signing three years ago, can grab his opportunities.
The Nigerian was unable to impose himself after serious injury last season and then missed the start of the current campaign due to a lack of match-fitness after the World Cup.
Moyes said: "It is not a goal I need from him - it is probably 12 or 15 goals.
"One goal isn't enough - but he has got to start with one to get more.
"He has played two and a half games, he is getting his chances and he has got to start delivering.
"But I'm looking at all the players."
Source: DSG
