Both McLeish and new joint vice chairman Sammy Yu have been discussing possible January transfer targets and the Ukranian striker, it has been reported, was one of the names on their shortlist.
However, when questioned about Blues being linked with the Dynamo Kiev striker McLeish has said that he knows nothing about it.
"Sammy has not told me that," he told Sky Sports News.
"I read it in the paper, but I've not heard anything about Shevchenko."