The Spanish goalkeeper joined the Reds from Atletico Madrid in June 2011 and after enduring media criticism for some of his early displays, he has firmly established himself as United's first choice between the posts.
The 23-year-old won the club's Player of the Month accolade for March, having assisted the comeback victory over Olympiacos with a superb double save at Old Trafford moments before Robin van Persie levelled the aggregate score.
The end-of-season prize is voted for by United fans and Cole, who gave goalkeepers a hard time throughout his seven years at Old Trafford, thinks De Gea has to be in with a shout of picking up the Sir Matt Busby trophy.
"When David first came to United he received absolute dog's abuse from some sections of the media. He was a young goalkeeper, it was a big-money move and he was coming to play for Manchester United - that must have been tough," writes Cole in his Ambassador's Column for United Review.
"It's a different culture, a different league with a different style of football. It was hard for him. But since that difficult first season I think he has been absolutely phenomenal. He has kept United in more than enough games this season and last season.