The Villans are currently rooted at the bottom of the Premier League table.
The Frenchman replaced Tim Sherwood at Villa Park in November, after a disastrous start to the season saw them sitting bottom of the table and winless since the opening day defeat of Bournemouth.
Thing did not improve under Garde’s leadership, with them having to wait until this week for his first win as manager, with them beating Crystal Palace 1-0.
With relegation still looking a certainty, there had been speculation about whether Garde would remain in the job, but McLeish has urged Villa to stick by him.
“I don’t know much about Remi, but he seems a sensible guy,” he told TalkSport.
“I think all managers should be give a decent chance and Garde should be able to state his claim as to whether he can get Villa back in the big time.”
“Garde has got a big fight ahead of him. If they are going to give him a chance he has to be able to rebuild it [the club].”
The problem for Garde will be that his side will have to hit the ground running next season for him to be safe at Villa Park.
If they are relegated to the Championship, they would surely be among the favourites to come straight back up given the squad at their disposal.
It is not an easy division to escape though, as former Premier League sides such Fulham, Middlesbrough, Blackburn and several others can attest to.
If they were to start slowly and struggle, it is easy to imagine that Garde could be an early managerial casualty next season.