Norris once again challenged the Dutchman during the closing stages of the Emilia Romagna Grand Prix, however, he ran out of laps to catch Verstappen.
With McLaren steadily gaining on Red Bull, the British driver could be in the mix for a win in Monaco this weekend.
Lando Norris achieved his maiden victory in MiamiThe McLaren driver came close to a second win in Imola
Norris suffers Monaco break down
Qualifying in Monaco is one of the most anticipated sessions on the whole calendar, with the driver who acquires pole position usually winning the race.
The tight and twisty nature of the circuit in this current era of wide F1 cars makes overtaking difficult, meaning track position is key going into the grand prix.
Before the weekend has even begun however, Norris suffered a failure whilst driving the streets of Monaco in his classic sports car.
The Brit took his classic Miura out for a spin in Monaco following his victory in Miami, but found himself coming to a standstill as his car broke down.
Speaking to the press ahead of the Emilia Romagna Grand Prix, Norris described the incident and how fans came to his rescue.
"It didn't start. But then the fans recognised me and they pushed my car and they bump-started it down the hill. So I was like mega," Norris said.
"Maybe if I didn't win the race they wouldn't have noticed me, they wouldn't have started it. So those are the perks in life. People can bump-start your car for you, in the Miura. That kind of thing."
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