Harry Redknapp is ready to let Keane leave White Hart Lane next month in order to make room for his own signings.
Aston Villa have been linked with a loan approach, which could include a £6million permanent option at the end of the season, but they could be rivalled by city neighbours Birmingham.
Blues have scored a measly 17 goals in the Premier League this season and McLeish wants to add some ingenuity to his attack.
He said in the Daily Mail: "I'm going to be working with the board to bring enhancement to the forward area. That's a priority.
"We want to enhance our assault on the second half of the season. I have a fast and athletic forward in Cameron Jerome and I have a tall forward with Nikola Zigic.
"I'm now looking for someone with a bit of guile and craft and I've identified that type of player."
