The new Villa boss wants to prevent another key player from leaving the squad while Ashley Young looks Manchester-bound.
Kenny Dalglish has been keen to sign the player for Liverpool as his primary attacking target of the transfer window.
“No chance do we want Stewart Downing to go,” McLeish said. “We certainly don’t want to lose Stewart - he’s a top player.
“I need to see what Stewart’s thinking … because I know that he made some comments when he was away on England duty.”
The 26-year-old winger, who has two years remaining on his contract, stalled on signing a new deal last month, saying that he wants the chance to play Champions League football.
“I am 26 and at a major crossroads in my career so I won’t be committing to a new deal at the moment,” he said.