'The Adventures of Rain Dance Maggie' group are coming to the Led Zeppelin guitarist's home country, England, in June and hoping he will appear on stage at one of their shows.
Drummer Chad Smith told the Daily Star newspaper: ''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. I saw him come on with Foo Fighters at Wembley.''
The band were forced to delay a string of concerts in the US earlier this year after frontman Anthony Keidis crushed a bone in his foot and had to undergo surgery, but he has now recovered and they are set to start playing again next week.
Chad added the time off was productive, as he got together with the other band members - guitarist Josh Klinghoffer and bassist Flea - to write new tracks.
He added: ''We just rehearsed and came up with some ideas and new song ideas.
''It's good for morale, it's good for the future. The future is bright.
''Normally in Chili Peppers world we never really had this much of a kind of break in a tour. Before, if we had a month off, we would never get together and write song ideas. But everyone just wanted to play. It was great.''
Red Hot Chili Peppers will start their tour in Tampa, Florida next Thursday (29.03.12), and they will play in the UK at Knebworth Park on June 23 and Sunderland's Stadium Of Light on June 24.