The Italian Champions League finalists have received an offer from Bayern of ??28m (???40m) for the Chile international midfielder, according to The Guardian.
Vidal, who won the Copa America with Chile this summer, would be seen as a welcome addition at the Allianz Arena as coach Pep Guardiola looks to strengthen his squad ahead of the new campaign.
Rummenigge believes Vidal would be a perfect replacement for Bastian Schweinsteiger, who signed for Manchester United earlier this week.
With the Bundesliga champions heading to China for an eight-day pre-season tour, Rummenigge told reporters at Munich airport: “I hope that Arturo Vidal will join us in the end.
“I can’t announce anything at the moment. If we sign someone, he would be a very good player.”
Rummenigge also confirmed that Mario Gotze would not be included in any deal to bring Vidal to Bayern, contrary to reports in the Italian press.