Wilcox has overseen the dismissal of Ruben Amorim and the hiring of replacement Michael Carrick as caretaker manager this week.
Meulensteen said on the No Tippy Tappy podcast: "Since INEOS and Jim Ratcliffe have come in, do they actually know what they're doing? You need to look at everybody in those positions, and they have to take responsibility in those important positions. Have they got the pedigree?
"If you look at Jason Wilcox (director of football) and how he’s ended up in that position, it was from being a youth coach, then ended up at Southampton, then you’re the technical director and the main man responsible for things at Manchester United.
"Imagine if Carlo Ancelotti came in to take the job, Carlo would take charge of the recruitment, because of his network and knowing what a winning culture looks like."
Meulensteen continued: "If I asked Jason, describe me a winning culture, what are the ingredients? Would he know? I'm a big Ancelotti fan, the way his teams play football and the success he's had, the way he carries himself and manages people.
"He would have the stature to come in and run a club like Man United. The problem is, who is out there that has the pedigree, understands the Premier League, has the ability to manage a club of that size, plays a certain style in a Man United way, and be successful?"