Speculation surrounding the Manchester United forward's future has been rife ever since he was left out of the starting lineup by Sir Alex Ferguson for the Red Devils' Champions League quarterfinal second leg against Real Madrid.
The Bundesliga outfit's honorary president has been a long-term admirer of Rooney, once describing him as "one of the world's greatest players".
"I would be very happy for Wayne Rooney to come to Bayern," the German World Cup-winning captain told reporters.
Pep Guardiola is set to take over the reins at the Allianz Arena at the beginning of next season and is likely to be given a substantial transfer budget to improve his alread formidable squad.
But United legend Bobby Charlton is confident that Sir Alex has absolutely no intention of letting Rooney, who has scored 15 goals in 30 games for the Red Devils this season, leave Old Trafford, while the manager himself has also denied that his star will be sold.