The bottom team in Italy's top flight have also swooped for Swiss midfielder Valon Behrami and Bologna striker Mattia Destro.
Perin joins Genoa, a club he played for five seasons from 2013 to 2018, on loan reportedly until the end of the June.
Behrami has also rejoined the northwestern team on a free transfer after leaving Swiss side Sion two months ago, with Destro undergoing a medical before a six-month loan deal.
Genoa are four points away from safety ahead of their home fixture with Sassuolo on Sunday.
Davide Nicola became the club's third coach this season last week after Thiago Motta was sacked having won just one league game since taking over on October 22.
Juventus legend Gianluigi Buffon's return from Paris Saint-Germain saw Perin pushed down to third-choice goalkeeper.
The 27-year-old joined Juventus in June 2018 on a four-year deal worth 12 million euros ($14.1 million), but he has played just nine games, and no games this season.
Former West Ham and Watford player Behrami has spent most of his career in Italy with Lazio, Verona, Fiorentina, Napoli and Udinese.
Former Roma striker Destro, 28, started his senior career at Genoa in 2010.