In 1998 he replaced Jan Magnussen at Stewart. This year, Dane Magnussen's son Kevin made his F1 debut for the top team McLaren.
Now Verstappen is hoping his own son is close to making the leap.
De Telegraaf newspaper reports that the reason for Jos Verstappen's Monte Carlo paddock visit was to talk to his F1 contacts about his son, 16-year-old Max.
Last year, Verstappen jr made the step from karts to cars, and in 2014 he is racing in the FIA's highly-regarded European F3 championship.
Verstappen has already secured his first pole and win, and so his well-known father was keen to spread the word among the decision-makers in the world of F1.
"It's nice to see that there is plenty of interest in Max," Jos is quoted as saying afterwards.
"His performances have not gone unnoticed, people are talking about him, and that's always a good sign," he added of Verstappen jr, whose mother Sophie Kumpen was a successful kart driver.
Toro Rosso rookie Daniil Kvyat raced in the European F3 series last year, and on the grid this year is Lucas Auer, the nephew of F1 legend Gerhard Berger.