Midfielder Ferguson is a strong candidate to be City's player of the year after an outstanding first season following a £1million switch from Rangers.
The 32-year-old has played a key role in Blues being on course for a top-10 finish in the Premier League and was chosen as the Sky Sports man of the match for Saturday's 2-1 home win over Burnley.
Ferguson believes he is capable of playing for up to another three years but he is keen for McLeish to also tie up his future with the midlands club.
He said: "I think it could be the start of good times here at Birmingham. I want to be part of it for as long as I can.
"I've got another year left here on my current contract but I am sure I can play for another two to three years.
I'm really enjoying myself at Birmingham and I'd love to finish my career here but obviously I'd like the manager to get his contract sorted out.
"Then hopefully, if he gets the backing, it could be good times ahead for Birmingham. You can see what the manager has done this year with a limited budget and limited resources."
Ferguson is hoping his own performances have silenced his critics.
He said: "I had to come down to England and play. I don't know whether it was to prove a point but maybe to shut a few people up and hopefully I've done that."
Fellow Scot James McFadden has hailed the impact made by Ferguson in his first season at St Andrew's and believes he has "fallen back in love with the game."
The former Everton attacker said: "In my opinion, Barry has been the best player for us this season. He has been consistent week in and week out and you know what you are going to get.
"He is never afraid to take the ball, a fantastic player, a great influence for the team.
"I think first and foremost he came here to get his love back for the game. It didn't go great for him in his last year at Rangers for whatever reason.
"There was a lot of expectation on him and the fans got on his back a little bit.
"I wouldn't say he has had a point a prove. I would say it was a case of getting back in love with the game and he has certainly done that this season. He has been excellent."
Burnley boss Brian Laws is backing his side to return to the top flight at the first attempt following relegation.
He said: "We've got a great opportunity to bounce back and take a leaf out of (the book of) the West Broms of this world.
"They have dropped out of the Premier League, kept the squad together, only lost a couple of players, and we've got the qualities and certainly got goals in us.
"The players have been on a losing streak, and in this division, teams can go on a real run of defeats. You can lose 10 games on the bounce.
"But you've still got to be believing and doing the right things and the players have tried their utmost to turn things around.
"You know we are not on a level playing field. Next season they will win a lot more games because they will be on a level playing field.
"The feelgood factor will be good for them because everyone likes to win games."