Mercedes is currently seeking a replacement for Ferrari-bound Lewis Hamilton, who will leave the Brackley-based squad at the end of the season to join the Maranello team in 2025.
Team boss Toto Wolff has openly admitted that he would want to have Verstappen but his comments drew criticism from Red Bull managing director Oliver Mintzlaff, who said Wolff's public flirting with Verstappen showed a lack of respect.
Verstappen signed a contract in 2022 to stay at Red Bull until the end of 2028 but speculation about his future has been rife amid the internal issues the Milton Keynes team has faced this year, including Adrian Newey's decision to leave in 2025.
Although an early move to Mercedes for Verstappen looks unlikely, Russell says he would welcome the challenge of having the three-time world champion racing alongside him.
"I'd be all for it," Russell said. "You know, coming into Mercedes in 2022 off the back of Lewis's legendary years and victories, that was a huge task for anybody jumping into a team where he's been for so long.
"I believe in myself, and you need to go up against the best in the same machinery and show what you have got, so I feel that having Lewis as my team-mate for the past three years... He's been a hell of a team-mate, such a great driver.
"And we push each other every single week and I think it's fair to say that, so I will welcome Max, I want to go up against the best. Everybody wants to prove what they've got, so make it happen."
Addressing the impact of Newey's departure from Red Bull, Russell added: "He's somebody who I respect. He is a legend in his own right with everything that he's achieved in the sport.
"You know, it doesn't change our life - unless there's a secret and he is coming to Mercedes, who knows?
"So, I think it was great seeing a lot of loyalty for a long time with him being at the team for 20 years. Lewis has been with Mercedes for 12 years.
"Sometimes people need to change, a change is a fresh start for both parties and it will be interesting to see what happens next."
