Ahead of Stoke's visit to Old Trafford this weekend, Pulis praised his counterpart.
"The manager is a living legend but I do not think people will give Alex real credit until he has left Manchester United," Pulis said.
"You look at their success and the way he changed things around. Perhaps he was fortunate because he was given the opportunity at the time to clear everything out.
"It took him three or four years to do that and then he built a base. The club has gone from strength to strength.
"Along with Matt Busby, they are the two greatest managers in its history."