McLeish is still to win over a significant proportion of Villa fans having defected from cross-city rivals Birmingham in the summer. His side have had a mixed campaign to date and sit 12th in the Barclays Premier League ahead of their Boxing Day trip to the Britannia Stadium.
Pulis feels fans must show patience towards the former Scotland and Rangers boss as the club remain in transition following the departure of their two previous managers in quick succession.
Pulis said: "I have got a lot of respect for Alex. It is a great job but it's a tough job and he has gone there from their rivals. It's never easy doing that.
"But have a look at his record, when he was up in Scotland and when he came down here. It's first class. Just give him time and patience. They're two very difficult words to stick to in football but he needs time, like we all do.
"He needs to time to put his mark and his stamp on the football club. Give him a couple of years and I am sure that club will be a strong, vibrant, successful club. You just can't turn it round overnight."