Norris, who finished third in Saturday's qualifying, less than three tenths of a second behind pace-setting world champion Verstappen, was asked whether he could pip the team who have dominated Formula 1 in recent seasons.
"I'd say yes," Norris told reporters after Saturday's qualifying. "It's so tricky, Sergio (Perez) is doing a good job. So there's one much harder car to kind of keep up with," he added.
Norris finished a distant second behind Verstappen at Japan's Suzuka Circuit last season, with his team mate Oscar Piastri in third.
"We proved last year, when we were further away from them, that we could keep in touch and not be miles behind. So that'll be our target for tomorrow," he said.
The Briton added, however, that he would also have to focus on holding off a chasing pack that includes Ferrari's Carlos Sainz, who won the last race in Melbourne, and double world champion Fernando Alonso of Aston Martin.
They qualified fourth and fifth, respectively, ahead of Piastri in sixth.
"Our competition is with the guys behind and at same time I'll do my best to push forward," Norris said.
McLaren team principal Andrea Stella said in terms of lap times the team had substantially reduced the gap to Red Bull.
"We definitely take some positive elements out of this qualifying... we know Japan suits our car characteristics," he said.
