An official announcement is expected Tuesday, according to the report.
Busch, 37, the only active driver with multiple titles, was not able to come to terms on a new contract at Gibbs where he has driven since 2008 and won two Cup titles while also building Toyota's most successful truck team.
M&M Mars is leaving NASCAR at the end of the year, and JGR was unable to find a replacement sponsor for Busch, who has offered to drive below his market value to get a deal completed.
It's unknown whether Richard Childress Racing has lined up sponsorship for Busch, according to the report.
RCR is currently a two-car team that has Austin Dillon and Tyler Reddick under contract for next season. RCR could expand to three cars to accommodate Busch, or could negotiate a buyout of Reddick who announced earlier this year that he's leaving to join 23XI Racing in 2024.
Busch admitted his contract status has been stressful in what so far has been a one-win season with career lows in most categories other than laps led.
Last week his engine blew with 22 laps remaining in NASCAR's opening playoff race after dominating at Darlington Raceway, leading a race-high 155 laps. So instead of a victory that would have automatically advanced him into the second round, Busch finished 30th and remained 11th in the playoff standings.
Busch has been on a bit of a publicity tour in what appears to be an attempt to show he can be personable, so he handled the Darlington disappointment with dignity in his live television interview. He praised his team for "all the stuff the guys have done and gone through, just all the news and everything that's going on all year, they've dug in and never given up."
Asked how he was feeling, he offered a faint smile: "I don't know. The sun will come up tomorrow."
The next race comes Sunday at Kansas Speedway, where Busch finished third in the spring on a dominant day for Toyota. His older brother, Kurt, won the race, and JGR teammates Denny Hamlin, Christopher Bell and Martin Truex Jr. finished fourth through sixth as Toyotas took five of the top six spots. Bubba Wallace was 10th in the only other Toyota.
Information from The Associated Press was used in this report.