The duo's comments came after Hamilton admitted he would love to sample a bike from the top tier of motorcycle racing, and that two wheels had in fact been his first love.
"Sometimes I speak with Hamilton - he came to the Grand Prix in Le Mans," said Rossi, who is chasing an eighth MotoGP crown this year. "He always says to me he wants to come [and ride] at my ranch.
"I asked him, 'But do you know how to ride or are you starting from zero?' He said that he has a good level of skill, he rides a 450.
"You need a bit of experience before you try the MotoGP, but our bike is very easy, so we will try to [tune out] a bit of power. For sure it is good if Lewis tries the M1."
Lorenzo, a two-time MotoGP champion, added: "Like [Rossi] says, [Hamilton] is very passionate about bikes. So yeah, with pleasure I will lend my M1 to him - maybe with a big insurance!"
Hamilton spoke about his passion for motorbikes in a recent interview with British newspaper The Daily Mirror, saying: "When I was a kid I wanted to race motorbikes. When my dad bought me my first go-kart I actually wanted a motorbike.
"I'd also love to test a MotoGP bike just to see what it's like. Naturally I'd know the lines but I'd love to know if I could even do it."
Unlike Hamilton, Rossi has first-hand experience of both MotoGP and F1 machinery, having tested for Ferrari on several occasions in the past. The Italian reportedly impressed on each occasion with his speed and technical feedback.