Ibrahimovic is largely regarded as one of the best forwards in world football, but often it is his antics on and off the pitch that draw headlines as opposed to his undoubted talent.
The rivalry between Marseille and PSG in French football has been heightened this season, with both teams vying for the Ligue 1 title.
And Fanni says he has regularly been annoyed by Ibrahimovic, who he feels is playing up to the attention he receives.
"I have had the desire to throw a punch at Ibrahimovic more than once," Fanni was quoted as saying by Le Parisien.
"We have said things to each other in English that I can not repeat in public.
"He is playing a role with his arrogant behaviour and he is doing it very well. They should give him an Oscar for it.
"He can be very annoying out there on the pitch, but that is a role he is playing. I know some PSG players and they all tell me that he is not really like that."
Marseille and defending champions PSG are both two points adrift of leaders Lyon, with the latter two meeting this Sunday.
