The 24-year-old has become disenchanted with his lack of first team opportunities in France, after making just three appearances this term.
Frei only joined Rennes from Swiss club Servette in January but a change in coach has witnessed a downturn in his fortunes.
Earlier this month, the forward urged Basel coach Christian Gross to end his misery and bring him back to Switzerland in the New Year.
With Switzerland having qualified for Euro 2004, Frei is desperate for regular action to cement his place in the squad and now Perugia could hand him a lifeline, according to reports in the Italian media.
The ambitious Serie A side are purported to have submitted an offer to Rennes with a view to taking Frei to Italy when the transfer window reopens in January.
Perugia's flamboyant president Luciano Gaucci wants to bring Frei to the club on loan, with the option of a permanent deal next summer.
Though the transfer would technically be prohibited in the New Year due to Frei being a non-EU player, Gaucci is confident he can obtain Uefa permission to complete a swoop by using a test case whereby a Swiss footballer was considered an EU member.
