Wassall has been placed in temporary charge of the Rams, after the dismissal of Paul Clement earlier this year, and he has made a good start.
The 47-year-old has arrested Derby’s slide, and stabilised their form - and Winterburn feels that Wassall should have a shot of getting the job.
“I think what you have to look at is to see where they finish this season,” Winterburn said. “If they go up automatically, a lot of their supporters would say he deserves the job.
“Under the old manager they liked to play out from the back, and I thought it was quite slow. If they do get automatic promotion, the club have got a massive decision to make.”
Wassall has won three of his first five matches in charge at Derby, and he has guided them team up to fifth place in the Championship table.
With 11 games to go, the Rams are seven points back from the automatic promotion spaces and they will require a strong run of form to make up that gap.
Derby did initially seem to have a chance to claiming a spot in the top two, but a terrible run of form under Clement’s guidance saw them fall away from the league leaders.
The Rams are now fighting to hold on to their play off spot, as they only have a five point advantage over Cardiff City, who are in seventh space.
Derby’s next match comes against Queens Park Rangers at Loftus Road later this evening.