The Scot, who scored 49 goals for the Londoners between 1989 and 1992, astonishingly claimed Big Sam can totally transform the club's fortunes.
McAvennie said: "Harry Redknapp went to Tottenham a couple of years ago and suddenly they were in the Champions League. I don't see why the same cannot happen to West Ham.
"They have definitely got the right man. My biggest gripe is why we failed to get him in January when we were still in the Premier League. But I have no doubts he will bring us straight back up."