Vettel, who's existing contract with Ferrari ends at the end of this season with speculations suggesting that the German might be moving to the likes of Mercedes.
A fifth victory of 2017 for the Briton would put the pressure back on Ferrari's Vettel and Hamilton can celebrate another milestone by bagging pole position on Saturday at the long and fast Spa-Francorchamps circuit.
Kimi Raikkonen on Thursday urged Ferrari to re-sign championship leader Sebastian Vettel and revealed that his love of racing was the only reason he had chose to continue next year.
Hamilton, who is trailing title leader Vettel by 14 points at 188, opined that Ferrari were faster in the race-simulation runs, but that his team are not lagging behind too much.
Earlier this week, team-mate Kimi Raikkonen also signed a new deal with Ferrari, with the Scuderia announcing another one-year agreement with the Finn on Tuesday.
Mercedes has yet to confirm its seconddriver, with Bottas joining in January as replacement for retired 2016 world champion Nico Rosberg with no guarantees for 2018. I am very happy we will keep working together. However, previous year he was obviously frustrated with an underperforming vehicle, leading to speculation about his future and links with a possible move to Mercedes.
"It definitely feels like a home Grand Prix for me because it's so close to the border", said Verstappen, sporting a special orange helmet this weekend. "So I find it hard to believe that they would change that".
"I think it was very spontaneous".
"I want the next nine (races) to all be (perfect)", he said.
"Mostly about other stuff to be honest", Vettel said.
Hamilton, who sportingly moved over for team-mate Bottas at the last round in Hungary to finish fourth, arrives here having finished on the podium just once in his last four outings.
Few things in F1 are as special as representing Ferrari at Monza in front of the tifosi and the pressure was on Vettel to deliver when he donned the famous red in Italy for the first time. "But it's been a good Friday, one of the better Fridays I can remember so I hope that carries on for the weekend".