Red Bull's Max Verstappen is the McLaren drivers' closest challenger in the championship, in third place, 21 points behind Norris.
But the Dutchman had a difficult day, qualifying only seventh.
Verstappen was unable to complete his final lap as Pierre Gasly spun his Alpine through 720 degrees at the final corner in front of him, but had managed only sixth fastest time on his first lap.
The Dutchman said Red Bull had been caught by surprise by the lack of grip in their car
"In qualifying basically everything felt bad," Verstappen said. "Every corner was a struggle, I just didn't have the balance. It was either understeer or oversteer. Even every single lap that I did I had a little bit different behaviour with the car. So yeah, that's not ideal.
"I didn't expect it to be this bad in qualifying, but I think no one did in the team. So, that's something that we have to analyse."
But Norris and Piastri both said they would not rule out Verstappen coming into contention in the race.
"Until he's out of the race, I don't think we're ever going to take Max out of the equation," Norris said.