The New Zealander qualified 18th at the opening race of the season in Australia, before crashing out of the race in the rain.
In China last weekend, he qualified last for both the sprint and the grand prix, and finished the two races 14th and 12th.
His average qualifying deficit to team-mate Verstappen has been 0.88 seconds. Verstappen finished second in Australia, third in the sprint in Shanghai and fourth in the Chinese Grand Prix.
Japanese driver Tsunoda was asked at the Chinese Grand Prix whether he would accept the promotion to Red Bull if it was offered.
He said: “Yeah, why not? Always. In Japan? Yeah, 100%. I mean, the car is faster.”
When the scenario was put to Lawson, he responded: “I’ve raced him for years, raced him in junior categories and beat him – and I did in F1 as well, so he can say whatever he wants.”
Lawson was promoted to Red Bull this season following the team’s decision to pay off Sergio Perez, despite the Mexican having two years remaining on his contract.
That decision was made after a difficult 2024 for Perez, who failed to finish on the podium after the fifth race of the season.
Perez’s performances contributed to the team finishing third in the constructors’ championship last year, behind McLaren and Ferrari.
As Perez’s slump in 2024 had mirrored a similar pattern of performance in 2023, Red Bull decided the time had come to get rid of him.
They had the choice between Lawson and Tsunoda as a replacement and chose the New Zealander, despite the fact he had completed just 11 grands prix split over two seasons – whereas Tsunoda has raced for the company since 2021.