After impressing as interim manager following the sacking of Jose Mourinho, ex-United forward Solskjaer oversaw a dismal end to the season as they missed out on a top-four finish. United finished the campaign with six losses and two wins from their final 10 fixtures.
But Van Persie said: "I think it's the perfect match, it's just they're having a bad spell…back in the day it was normal for a manager to get time. Nowadays if you lose six games, you're out. Is that the solution? Give someone time, especially if it's a kid from the club."
"It's funny because when he started everyone was so positive, they were winning and they made a miracle by beating PSG," said Van Persie, who and scored 58 goals in 105 games for them between 2012-15.
"Everyone was screaming like, 'Give the guy a permanent deal'. And then since that permanent deal the luck went away a little bit; they've been losing more games than they want to.
"But he got a three-year deal and everyone should look at the bigger picture. His presence, the way he presents the club, is the proper way in my opinion. He's positive, he wants to achieve big things with the club and that is the only way forward.
"He's a man of the club, he played there for more than 10 years, he won the Champions League - actually his goal got them the Champions League - so he has a big part over the years at the club.
"He's been a coach of the reserves, he is Manchester United. Similar, in a different way, to Ferguson. He was Manchester United and Solskjaer is Manchester United as well.
"Everyone has that at a certain time. He had a fantastic first period - now the last 12 games have been tough. OK, but next season they have to pick themselves up and go again."
Van Persie , having spent eight years playing for Arsene Wenger's Arsenal, and he believes the pair prove the importance of patience.
That is a value he feels should also be applied towards players, suggesting United's current problems will not necessarily be solved by more heavy spending in the transfer market.
"In that way I'm a little bit old school," the Dutchman argued. "Major changes, what do they do? Arsene stayed at Arsenal for 22 years, Sir Alex at United for 26 years.
"If he wants absolutely the best and only the best for the club, give him time. Is it going to change, to find a new manager now after a bad run? And then, so what, he will have a good start and then they will be in the same position.
"Nowadays, as well, if you look at the news, if you hear stories, it's so business-wise.
"If a player has a couple of bad games, 'OK, sell him!'. If he doesn't score a few goals, 'OK, he's out, he's finished'.
"Back in the day you used to get time, you can make mistakes, you can learn. Now I get the feeling that time is less. Ideally, you would get time - as a player, as a coach."