The former West Ham hitman, speaking exclusively to Football Insider, insists the Magpies need an experienced head steering the ship.
This site understands Newcastle are in advanced talks to appoint Michael Emenalo as their director of football after a breakthrough in discussions.
Following Newcastle’s Saudi-backed takeover, Staveley and her husband Mehrdad Ghodoussi were charged with running the club day-to-day.
However, speaking to The Athletic (8 October), Staveley admitted “If we don’t do a good job, we won’t be running the club.”
McAvennie claims Newcastle need football people running the club and admitted his relief that Staveley could step aside.
“I’m glad they are getting a director in,” McAvennie told Football Insider correspondent Ben Wild.
“No offence to Staveley but she has done what she wanted, she owns the club.
“The club needs to come first now, let football people run the football club.
“I’m not sure she is the right person for that. She was the right person to get the deal through.
“That is her speciality. From what I understand she has no experience of running a football club.
“We are talking about serious money and serious players, they need someone experienced pulling the strings.
“It’s nothing against her. Newcastle are the richest club in the world now and they need experience to steer that ship.”
Eddie Howe became Newcastle manager on Monday afternoon as Staveley signed off on her first major signing of the new era.
His first game is against Brentford after the international break.