New Blues vice-chairman Sammy Yu has been drawing up a shortlist of players with McLeish ahead of the January transfer window.
However, McLeish insists a move for Shevchenko has not been discussed and that he hopes to bring in three or four players in January to strengthen the squad at St Andrew's.
Asked about the link with Shevchenko, McLeish told Sky Sports News: "Sammy [Yu] has not told me that.
"I read it in the paper, but I've not heard anything about Shevchenko."
McLeish is working hard on bringing new faces to the club and he believes new additions are needed to improve the squad.
"We have got to see if certain players want to come to Birmingham as well as a load of other obstacles, but we will try and enhance the squad, enhance the quality with three maybe four players," added McLeish.