Father and son sat down with the boss of Red Bull's prolific driver development programme, Dr Helmut Marko, but reportedly ultimately decided to sign with Mercedes.
Italy's Autosprint said recently that Verstappen jr hopes to make the move to GP2 for 2015, but in the meantime could shortly make his F1 test debut.
However, Italiaracing reports that the story of Verstappen's dramatic arrival on the formula one radar may have taken a sharp twist at the weekend.
As the Red Bull Ring hosted the latest F3 round, the Verstappens apparently had a "long meeting" with Marko.
Austrian Marko, a high profile member of Red Bull's premier world championship-winning F1 team, then joined the Verstappen camp on the F3 race grid.
The upshot is that "Red Bull is willing to pay the (contract) penalty" to sign the young Dutchman to its programme, Italiaracing claims.
And that's not all. Marko has reportedly promised Max, who will be a mere 17 at the time of the 2015 season opener, his F1 race debut in a Toro Rosso next year.
Verstappen would most likely take the seat currently occupied by Jean-Eric Vergne, who has been at Toro Rosso for three years but is being overshadowed in 2014 by the 20-year-old rookie Daniil Kvyat.
It was believed Vergne's seat would be filled for 2015 by another Red Bull-backed hotshoe, Carlos Sainz jr.
As the 'silly season' shapes up, however, there are other possibilities. Perhaps Verstappen and Sainz will be paired at Toro Rosso, while Russian Kvyat moves to Red Bull Racing.
"Daniil has been sensational so far," Red Bull team boss Christian Horner is quoted by the Spanish sports daily AS.
With McLaren pushing hard to sign a top driver like Sebastian Vettel, Red Bull could pair its on-form surprise of the 2014 season, Daniel Ricciardo, with Kvyat.
Horner, however, played down the possibility of a driver change for 2015.
"We have 100 per cent the best driver pairing in formula one," he told Sport Bild.
"Seb is comfortable with us, trusts us. He has won 38 races with us and you don't forget that easily.
"And I don't think Seb actually wants to go somewhere else," Horner insisted.