Hakkinen raced in F1 from 1991 to 2001, a period in which F1 mostly had a single tyre supplier, but his 1998 title came with McLaren on Bridgestones and Ferrari using Goodyear.
The double world champion was back in the F1 paddock in Japan last weekend, having demonstrated his '98 McLaren as part of the 20th anniversary celebrations of his first title.
Asked what he likes about F1 now and what could be better, Hakkinen warned that it was easy to find "a lot of things that you can look at and think 'ah, that should be different and that should be different'".
He said that as he "cannot change it, it's better not to focus too much", but admitted he would like to see current tyre supplier Pirelli have a rival.
Pirelli has been the exclusive manufacturer since 2011, while F1 has not had two tyre manufacturers since 2006 and will remain a single-supplier series until 2024.
"There is no competition – there should be other manufacturers out there, that way the competition comes up," said Hakkinen.
"When I speak to the drivers I have understood the tyres go on a certain peak and if you push even a little further they just overheat.
"It's not a criticism of what Pirelli's doing, it's just a fact that there should be competition.
"If you only have one driver driving out there it's the same thing. We need competition. That's exciting."
Hakkinen's other recommendation for modern F1 was to provide more track time for rookies.
The Finn graduated to F1 from F3 with Lotus, with minimal testing experience, but spent most of 1993 on the sidelines as McLaren's test driver.
That paved the way for the race seat with the team he spent the remainder of his F1 career with.
However, on-track testing opportunities are limited in the modern era, with most of the development conducted via simulation.
Hakkinen said: "[For] young drivers that come into F1 it's quite challenging because there is no testing.
"In my opinion it could be much more useful if the young drivers can test and develop themselves.
"Whatever sport you do, if you cannot practice, how do you improve?
"Of course the technical side of the cars, how do you develop the engine and chassis if you're not allowed to test?
"Yes, of course you can go into computers and simulations but they are not in a real world."