A return to the Bundesliga, where he shone for Hamburg before moving to Spain, is said to appeal to the 27-year-old.
Robben claims his Holland international team-mate would jump at the chance to head back to the Bundesliga, with Bayern his preferred destination.
Robben made the switch from Real to Munich last summer and believes his countryman would be advised to follow in his footsteps this year.
"Rafael told me that FC Bayern is a great club when we were playing together at Real Madrid," he told Kicker magazine.
"Rafa was also the one who advised me to come to Munich.
"He has told me that, if Bayern were to ask him to come, he would cycle to Munich just to get a contract here.
"He wanted to move to Munich (when he went to Real) so maybe it could still happen."