The 27-year-old striker has been linked with a move away from Old Trafford since it was revealed he had a transfer request rejected by the Premier League champions towards the end of the season.
Van der Sar, who is now a marketing director with Ajax, feels Rooney could find a new lease of life under incoming United manager David Moyes.
The Dutchman told BBC Radio 5 Live's Sportsweek programme: "There has been so much pressure on him, you build him up and put all your money on him to make England world or European champions."
He added: "So it's also quite easy to cut him down again. Players have indifferent seasons and maybe Wayne's been overtaken by Robin van Persie this year but it's the hard work that he puts in for the team (that should be recognised)."
Rooney scored 12 league goals to summer signing Van Persie's personal haul of 26 in the 2012-13 campaign.
"It was maybe a lesser season (for Rooney) and he didn't play the last couple of games but he's really important for United," Van der Sar added.
"English players tend to stay in England to play their football and rightly so because you have big clubs, the tradition and the stadiums are always full.
"With the change of manager and backroom staff it could be a big change for Manchester United but I don't think you'll find a better atmosphere at many other clubs."
- Sports & Recreation
- Van der Sar