Other candidates for the vacant position are Mick McCarthy - whose Ipswich Town side have an outside shot at the Championship playoffs this term - and ex-Swansea boss Garry Monk.
Sean Dyche, the Burnley boss who took the Clarets up to the Premier League and back down again last season, is another candidate although Villa face a battle to pluck him from Turf Moor.
Steve Clarke, most recently at Reading, is available - as is recently-sacked Newcastle manager Steve McClaren.
And Steve Bruce could reportedly be open to leaving Hull for Villa Park if the Tigers fail to secure promotion this season.
Caught off Garde - Remi leaves Villa
Meanwhile, former Manchester United goalkeeper Peter Schmeichel says Villa should never have sacked Tim Sherwood - the man Garde replaced back in November.
Former Tottenham coach Sherwood guided Villa to the FA Cup final last season and helped them avoid relegation.
But he lasted just four months into the new season.
"I'm shocked that you give a manager a job in a very difficult situation, that he hasn't put the club in, and then you give him that little time to solve it?" Schmeichel told Sky Sports.
"They should have done their due diligence and got it right back then.
"Tim Sherwood was well capable of getting Aston Villa out of trouble, but they didn't think that and now they've gone down the route of sacking yet another manager and history proves that doesn't help.
"So, it's a shock and then again no, because that's the way football has been going for quite a while."
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