Van Persie's future at Old Trafford has been the subject of speculation over the course of the season after David Moyes replaced long-serving manager Sir Alex Ferguson in May.
Moyes' position is also under question following a trophy-less campaign, which has United on the verge of missing out on the UEFA Champions League for the first time in 19 years.
Netherlands coach van Gaal is tipped to move to the Premier League after the FIFA World Cup in Brazil, with Tottenham and United rumoured destinations.
And Hooijdonk, a former Dutch international, said van Gaal's arrival in Manchester would be great for van Persie, who is battling to overcome a knee injury.
"Let me tell you one thing: if van Gaal becomes manager of Manchester United, van Persie will stay," the former Celtic striker said.
"Louis will bring in a number of top players and he will create a whole new team for United – which, we can see, is necessary."
Van Persie has endured an injury-interrupted second season at Old Trafford but he has still managed to score 11 goals in 18 Premier League appearances.
