“We brought him in to play, and when he has played he has done well,” Rummenigge said at the Festival of Sport in Trento, Italy.
“He has scored a few goals. [Kingsley] Coman and [Serge] Gnabry are exploding, but Ivan is always good.
“I won’t rule [signing him permanently] out, he has had a good start to the season. We have an agreement with Inter to talk about it later, and we will also evaluate it with the player.”
Perisic was signed in part due to the summer exits of legendary wide duo Arjen Robben and Franck Ribery, with manager Niko Kovac undertaking a significant rejuvenation project at the Allianz.
He has been an immediate hit in Florence, and recently starred with a goal in a 3-1 win over AC Milan. After a terrible run of 24 games without a win stretching back to last season, things are looking up for Fiorentina, who have now won three league games in a row.
“Montella made a smart move,” Rummenigge said. “Fiorentina have played with two strikers and given Ribery licence to attack without forcing him to defend, so he can concentrate more on attacking.
“Against Milan he scored a masterpiece of a goal. He was always very good, it wasn’t by chance that he played for 12 years at Bayern and won everything.
“It surprised us a little that he went to Italy with Fiorentina because everyone expected him to go to Saudi Arabia or China, but he made a footballing decision and I’m glad he’s doing so well at Fiorentina.”
On the subject of Serie A, Rummenigge also had praise for new Inter boss Antonio Conte, predicting that the former Chelsea boss could win the Italian title.
“I have been watching, their start has been good, apart from the match against Juventus. He can win the Scudetto,” he said.
“Conte is doing a good job. It is important they have a quality and trustworthy technician like him, and against Barcelona I saw a good game where Inter deserved to score another goal. Barca were lucky to win. Inter are a newly rebuilt team, it takes a little patience.”