Guzan's current deal runs out at the end of the campaign and he has struggled to establish himself as first-choice keeper during his four years at Villa.
But he impressed McLeish during a run of seven Premier League games in December and January when the current number one, Shay Given, was sidelined through injury and that led to the new offer.
McLeish said: "We will give Brad time. It depends on how long though. We have certainly made the offer and we respect that Brad needs time to mull it over. I understand the dilemma he is facing, but at the same time it is not like he is second in command to Joe Hart, who is only 24.
"Shay is 35 now and, when Brad has come in, he has proved himself to be a Premier League keeper. Now we know he is Premier League class. Brad probably realises if Shay has a niggle or a problem, or we are going to do anything in the cup competitions, we are going to put him in."
Villa have already opened talks with defender Carlos Cuellar over a new contract after his recent impressive form.