The deal has intrigued United legend Stepney, a hero in goal of the 1968 European Cup triumph against Benfica at Wembley.
Stepney told the Daily Star Sunday: "The secret of succeeding at Old Trafford as a goalkeeper is not to be flash, do your job - and keep clean sheets. If a keeper does that, he will quickly get the crowd on his side. It was like that in my day and it is like that now, because United have always been the biggest club in the country and Old Trafford the biggest stage.
"There have been some classic cases of keepers not starting well at United and if that happens, it can be a struggle.
"But the thing about him is that he hasn't come from the lower divisions. He has been playing against clubs like Real Madrid and Barcelona, so from the start he has been used to facing top opposition on big stages.
"In 40-odd games in La Liga this season, he has kept 24 clean sheets and that is impressive. And if Sir Alex thinks he's the one to take over from Van der Sar - which is a big task - then that speaks for itself."
Stepney added: "He is clearly young and promising and has been described as the best young goalkeeper in the world - but he still isn't a full international. That's because Spain have goalkeepers like Iker Casillas at Real Madrid and Pepe Reina at Liverpool but if De Gea does well at United, I am sure he will get his chance with his country."