The band said that they are big fans of the legendary guitarist and would love him to perform on stage with them during their shows at Knebworth and Sunderland's Stadium of Light this summer.
Drummer Chad Smith told the Daily Star: "Jimmy Page has come to our shows before but we haven't had a chance to play with him. That would be really cool so maybe that can happen.
"Maybe we can get Page to come out to Knebworth. I saw him come on with Foo Fighters at Wembley."
Smith also revealed that the band are particularly excited about performing at the Knebworth site as it has previously played host to a number of iconic rock acts.
He added: "Being a big rock fan, Knebworth is particularly exciting. I first heard about Knebworth when Led Zeppelin played there in 1979, so to me it's hallowed ground and pretty cool that we will be following them.
"Black Sabbath, Deep Purple, The Stones and Queen and The Who - I grew up listening to all of them. To go on over to be accepted where these guys play blows our minds. It's like a bucket list kinda thing, we can tick that one off."
Red Hot Chili Peppers will play Knebworth Park on June 23 and Sunderland's Stadium Of Light on June 24.
> Dizzee Rascal to support Red Hot Chili Peppers at Knebworth show
Watch the music video for Red Hot Chili Peppers' 'The Adventures of Rain Dance Maggie' below: