McLeish has up to £40million to spend in the January transfer window, says News of the World.
McLeish have put McGeady high on his hit-list ahead of the January transfer window.
Birmingham have also had scouts watch Bosnian international strikers Ednin Dzeko and VEdad Ibisevic and Serbian forwards Milan Jovanovic and Nikola Zigic this weekend.
McLeish said: “I still think we are bit thin in the wide areas and up front.”
He added: “If I was to say to Carson that I would like to spend £10m on a top, top striker then we have got to convince everybody that is the right man.
“I will try and be as careful with the money as I can, but I know we are trying to bring in another level of player so maybe we are going to have to spend a little bit more in terms of the overall package.
“If we have got Premier League ambitions then we need to bring in the quality.”