Dein was in charge at the Gunners for many years, including the time when legendary coach Arsene Wenger was hired in the 1990s.
He was asked about the fact that United and Liverpool have both been put on the market by their owners, the Glazer family and Fenway Sports Group respectively.
He told Sky Sports: "I've got my own personal view. Both clubs were involved in the 'Super League' and I think they [the owners] felt that was the holy grail for them.
"When that failed and they saw it would be another hard slog to move the club forward again after that, that may be one of the reasons.
“It's important the Premier League is stable and has good owners."