Liverpool had an improved bid of £15 million rejected by Villa earlier this week and there have been strong suggestions that the Reds will up their offer for 26-year-old.
With Ashley Young having already been sold to Manchester United, Villa are unwilling to lose a second England winger and McLeish revealed he has already told Downing that he features in his plans for next season.
"I understand why there's teams interested in him and that is what happens when you play well consistently," McLeish told the Birmingham Mail.
"His performances last season were top drawer. That's why he's not for sale. The club don't want to sell him.
"I spoke to him briefly last week and I intend speaking to him again when all the lads are back in for training."
Former Villa manager Martin O'Neill signed Downing from Middlesbrough in a £10 million deal in the summer of 2009.