Allardyce, who was in charge of the club last season, believes that his former employers may have an issue with unhappy players at Goodison Park this season.
"One of the problems they may have is all the excess players they have on the books," Allardyce told Sky Sports News.
"It was a big problem for me, these 10-12 players that we could not look after in a squad of 24, and that creates a lot of problems.
"And I have not seen too many players actually going out and the players that they would like to go out are not moving as quick as they would have expected."
Everton still remain on course to secure a late loan deal for Chelsea defender Kurt Zouma after processing a deal sheet with the Premier League to be given an extension to 7pm.