The club confirmed there was an agreement in principal, but has yet to confirm the signing of the 38-year-old former French international and Bayern Munich star.
Ribery has been a free agent since Fiorentina chose not to renew his two-year contract in the summer.
"FR7" will arrive in Salerno on Monday to undergo a medical examination and "then he will sign a contract that will bind him for one year to the Dark Reds, with an option of extension," said the 'Corriere dello Sport'.
The Rome sports daily reported the club would pay Ribery 1.5 million euros for the season and had lined up housing for him.
"There is an agreement in principle, we are waiting for the ratification," said Angelo Fabiani, sports director of the club, quoted by 'Corriere dello Sport'.