Hamilton told reporters in Japan this month that he planned to race beyond 2023 and expanded on that recently by saying he and Mercedes would do another deal.
"We're going to sit down and we're going to discuss it in these next couple of months, I would say," the sport's most successful driver, with a record 103 wins, told reporters at last weekend's US Grand Prix.
Russell, who replaced Valtteri Bottas (33) in the lineup this season and is ahead of Hamilton in the drivers' standings with three races to go, welcomed that prospect when asked at the Mexican Grand Prix.
"It's really exciting to have that potential of Lewis staying on for a number of years to come," said the Briton, who has yet to win a grand prix.
"He's proven that he's definitely not lifted his foot off the throttle pedal and he's definitely in the last few races performing probably better than ever.
"That's really exciting for me to have that opportunity to be his teammate and to go directly head to head with him and grow on this journey we're on together."
Mercedes were the dominant team in Formula One, winning eight successive constructors' titles until dethroned by Red Bull this season.
Hamilton and Russell have been wrestling with a difficult car, that suffered bouncing early on, and have yet to win a race in 2022.
Russell said he felt the two drivers had a great relationship and were working together with the team to get Mercedes back to the top.
"It would be great to be team mates for a number of years to come," he added.
