McLeish seems certain to be amongst the contenders when some of the big managerial jobs come on the market after three years of success at St Andrew’s.
He has led Blues to promotion, their highest ever top-flight finish – ninth – and now a shock cup success over Arsenal at Wembley last weekend.
But he is adamant he has unfinished business at Birmingham ahead of Saturday’s Premier League clash with visiting West Brom.
He said: “I just signed a new contract after protracted talks and I am happy at Birmingham.
“It is a great start for me in terms of winning a trophy here inside three and a half years.
“It is something I never thought we could achieve in such a relatively short time but we are still developing.
“We still have a lot of work to do. With the right organisation and planning, we can go onto better things.”
McLeish insisted ensuring top flight survival is the only thing on his mind when asked if he expects to be linked with other clubs.
He said: “I’m not even thinking about that at all. That couldn’t be further away from my mind.
“It is possible (to be linked) but I’ve got other battles to make sure we win over the next few weeks and that is my focus.
“I know this game is so fickle that you are as good as your next result.”
McLeish added: “It is not inconceivable we could have lost the Carling Cup and still got relegated.
“You can paint the picture whatever way you want but our goal has always been to retain Premier League status.
“If I get the titanic and heroic performances I saw last Sunday in the games from now to the end of the season, we believe we will be a Premier League team next season.”
McLeish is confident the character of his players means they will not become complacent after their cup triumph.
He said: “I don’t think we will take our eye off the ball. I do believe the players have the mindset to realise what is at stake.
“It’s whether we can cope physically with the demands of the cup competitions and especially the toll it took last week.
“But I do believe the mindset of the players is right for the assault on this league game at the weekend.
“Stephen Carr is grumpy again so that means everything is back to normal!
“I can’t guarantee anything but I know in the past people coming off a cup run might put their tools away the next week and rest on their laurels.
“I don’t believe this group will do that.”
McLeish Happy To Stick With Blues