Verstappen has won eight consecutive races since standing atop the podium at the Miami Grand Prix in May. Should he repeat the feat at Zandvoort, he will draw level with former Red Bull driver Vettel.
The four-time champion scored his record run at the close of the 2013 season, as he secured the last of his four world titles.
After qualifying on pole for the Dutch GP and having already overtaken Vettel as the driver to secure the most race victories in Red Bull colours, Verstappen was asked what it would mean to level this astonishing record.
“I think after like five wins in a row or something like that, Seb texted me, ‘well done, what you're doing at the moment, keep it up’ and something like ‘you’re going to do it’,” said the Dutchman.
“But I was like, ‘that's nine wins in a row, it’s something very impressive’ and I never thought I would be able to be already on eight.”
Verstappen has taken home race-winning silverware on 10 of 12 weekends so far this year, with two further successes coming in the three sprint races. On Sundays, his two other results have seen him take the chequered flag in second, with his worst result being third in the Azerbaijan sprint.
The 25-year-old’s previous best streak came last year, with five wins from France to Italy en route to his second drivers’ crown.
Playing down the importance of levelling Vettel, Verstappen added: “If it's possible of course I’ll go for it, but it's not something I have in the back of my head, constantly like ‘I need to do this, I need to do this’.
“I'm not in this sport to try and break records. I'm just here to win at the moment.”
Should Verstappen draw level with Vettel at Zandvoort, he will only have to wait one week for a chance to take the record outright, when F1 makes its annual pilgrimage to Monza for the Italian GP.