The Frenchman's future is in doubt with Villa on the brink of relegation from the Barclays Premier League for the first time in their history
Hollis and the new Villa board - which includes former Football Association chairman David Bernstein - are conducting a review of the club after their disastrous season, which has seen them win just three league games
Chief executive Tom Fox resigned on Thursday just 48 hours after sporting director Hendrik Almstadt left.
Villa are bottom of the table, nine points from safety with eight games left ahead of Saturday's trip to Swansea, and Hollis conceded he cannot issued any promises over Garde's future
"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," he said
"Remi is fully engaged. He is spending a lot of time with Mervyn (King) and Brian (Little) and David. I'm leaving it to them to see what works best. They will come up with their recommendations."
More changes are expected at Villa Park as they prepare for their first relegation from the top flight since 1987 with every department under the microscope
Hollis said: "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."
But Hollis admitted the previous regime had missed its targets which is why he felt the need for change
He added to Sky: "You can't say it's gone right. These kind of organisations are about winning football games. We've not been winning football games and hence we have been very open that we're trying to take action and put things right. Hopefully we will return to better times."
Source: PA