A full review of the club is underway, and Hollis has said no decision on the manager's future will be made until that is complete.
Hollis was appointed as owner Randy Lerner's replacement at chairman of the Premier League bottom side in January, and has already made a host of sweeping changes at the club.
Lifelong Villa fan and former Bank of England governor Mervyn King has been appointed as a director at the club, along with former FA chairman David Bernstein, and Villa hero Brian Little.
One question which has remained throughout recent events is that of the future of Garde, who has overseen just two league wins since taking over from Tim Sherwood at the start of November.
King suggested earlier this month that the real question would be whether the Frenchman himself wants to stay at the club beyond the end of the season, but Hollis appears to have suggested that the decision may yet be taken out of the manager's hands.
The chairman told Sky Sports: "Let's see where the review goes. Let's not pre-empt anything. Let's give the process the time it needs to make the decisions. They're not going to make knee-jerk decisions.
"Remi is fully engaged. He is spending a lot of time with Mervyn and Brian and David. I'm leaving it to them to see what works best. They will come up with their recommendations.
"There's no vendetta going on here. This is about turning over every stone in the club and no-one individual is bigger than the club, including me. What we will do as a part of the review is look at everyone's role and see how that fits in as a part of the package that we are going to be putting together than takes this club forward."
Villa look certain to lose their ever-present Premier League record and suffer a first relegation since 1987 after winning just three Premier League matches all season.
The former European Cup winners are nine points adrift at the bottom of the league table with just eight matches remaining.