According to Sky Italia, Inter have rejected the offer but talks are continuing between the clubs.
Inter want €15m for Perisic, 31, and there is a feeling that in the end an agreement will be reached.
Bayern had an option to buy the Croatian winger for €20m, but felt it was too high given his age.
However, Hansi Flick has made a request to Inter chiefs to sign Perisic on a permanent basis.
Perisic started and scored in Bayern’s historic 8-2 drubbing of Barcelona in the Champions League semi-final.
He came off the bench for the last 22 minutes of the final when Bayern beat PSG to lift the trophy.