The team - which is yet to comment or make an official announcement - is reported to have made the move after just two races in the Formula 1 season.
According to both BBC Sport and Sky Sports News, Tsunoda will replace Lawson, starting with next week's Japanese Grand Prix.
Lawson, 23, has had a difficult start alongside teammate Max Verstappen, and he will be moved back to the company's junior squad Racing Bulls.
The young racer was knocked out at the first of all three qualifying sessions, and didn't score a single point in Australia and China.
Meanwhile, Tsunoda - who signed with Red Bull's sister team in 2021 - will step up after previously missing out as Sergio Perez's replacement.
Following the Spring and Grand Prix sessions in Shangai, team principal Christian Horner praised Lawson while acknowledging the "very tough" situation, as well as Red Bull's duty of care to the racer.
He told press: "I think Liam still has got potential, we're just not realising that at the moment. I think the problem for him is, he's had a couple of really tough weekends, he's got all the media on his back.
"The pressure just naturally grows in this business, and I feel very sorry for him. You can see it's very tough on him at the moment.
"He's a young guy, we've got a duty to look after him and we're going to do the best that we can to support him.
"Liam's still a very capable driver. We know that, just for whatever reason, we're not seeing him able to deliver that at the moment."