The Red Devils are still in the FA Cup and Europa League, with the latter also offering a route into the Champions League.
But Van Persie says that winning cups is not enough, as Solskjaer must ensure United are winning with style.
The Dutchman, who won United's last Premier League title during the 2012/2013 season, told reporters: "Question marks over Ole will remain unless something changes, even if they win the Europa League — the standards are that high.
"It would help take some pressure off, but the club have been winning over so many years and everyone remembers the Ferguson era.
"His philosophy was about taking risks and playing entertaining football and that's what United fans expect.
"When you play there that's the pressure you have to get used to. Winning is not enough — you have to win in a nice and attractive way."