The Frenchman was sacked by the club last week after a dismal spell in charge.
The Villans are currently looking for their third manager this season following the sacking of Remi Garde last week.
He was sacked following a dismal spell in charge after replacing Tim Sherwood back in November.
The club are not looking to appoint his replacement until relegation to the Championship is confirmed however, preferring to start with a clean slate after the disaster that is this season.
Sutton though, believes a new manager should be brought in immediately to start building for the future.
“They (Villa) have been disgraceful. I think they need to get a new manager in now and start building,” the Birmingham Mail reports him saying.
“Whether Villa can then offload players in the summer. There will be a lot of mercenaries there who will want to move on.”
“It might not be that easy, though, hence why I think it makes sense to get someone in now. Be ruthless, and start to build for next season.”
Who Villa appoint as their next manager is arguably one of the biggest decisions they have had to make in a number of years.
The consensus seems to be that they need a man who is comfortable and experienced in the Championship as they prepare for life in that division next season.
A leading candidate is currently former Leicester City manager Nigel Pearson, who would certainly fit the bill based on that criteria.