After losing out to the Red Devils in the Barclays Premier League and Champions League, the futures of Grant and a host of key players - including the likes of Didier Drogba, Frank Lampard and Ricardo Carvalho - have been called into question.
But Venables believes his former club would be best served by a summer of stability.
"No-one could have done a better job than Grant given the circumstances of the job he inherited after Jose Mourinho was sacked," the former England boss told The Sun.
"His work has been largely unappreciated and, because he replaced the Special One, he has cruelly been treated as public enemy number one.
"It's hardly fair - but then football's not fair."