The group covered Oasis' 'Stop Crying Your Heart Out' at this year's V Festival, following the Manchester rockers' decision to pull out of their headlining slot.
Rice-Oxley told the Daily Star: "I often wonder if Noel is almost resisting the truth that Keane and Oasis are alike in a lot of respects. I think we share a lot of fans. We are both bands of the people.
"People love coming to a Keane show and an Oasis show because there's a directness to the songs and people come together in a very communal way."
He added: "It would be great for Noel to produce us - I offer the olive branch. We're huge fans."