Reds boss Kenny Dalglish has had England winger Downing at the top of his wanted list for several weeks and is not ready to give up now just because there has been a regime change at Villa Park.
McLeish, however, is determined to keep Downing as he tries to head off a fans revolt at the club - Villa are set to lose Ashley Young to Manchester United and Downing's exit would not go down well with fans who are already fuming that former Blues boss McLeish is now in charge.
"No chance do we want Stewart Downing to go. We certainly don't want to lose Stewart - he's a top player," McLeish explained.
Dalglish has money to spend and a winger is one of his top priorities so he has no intention yet to give up his pursuit of Downing and it will come down to whether the Blues board accept the Reds offer for the player.
Liverpool also remain interested in Wigan's Charles N'Zogbia as a possible alternative to Downing.