Rooney, 31, continues to be linked with a lucrative switch to the Chinese Super League, having found himself on the outer at United.
But that has left former United team-mate Keane bemused, with the Irishman saying the club and England captain should be staying in Europe.
Keane added: "Going to China? Madness.
"He's 31 years of age, there's plenty left yet for Wayne Rooney to do in Europe."
Rooney, United's all-time leading goalscorer, has netted five times in 29 appearances in all competitions this season.