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Ribery, now 38, is currently playing for Salernitana but the club are looking to offload him due to their financial situation.
Le Parisien say Ceara, who play in the Brazilian top flight, were contacted regarding Ribery's availability.
Robinson de Castro, the club's president, was not even aware the former France international, was still playing.
"Yesterday they called me to offer me Ribéry," he said, as per GFFN.
"I didn’t even know he was still playing!” de Castro said. “Are we going to try to recruit him? I don’t know.”
Ribery joined newly promoted Salernitana in the summer and was appointed their captain, making 12 appearances for the club, who are bottom of Serie A on 8 points from 18 games.
He signed a one-year deal after leaving Fiorentina, where had played 51 times and scored on five occasions.
Ribery spent 12 glorious seasons at Bayern Munich, scoring 124 times and winning an incredible nine Bundesliga titles as he and Arjen Robben tore it up down the flanks.
He was also an integral part of the club's treble-winning side under Jupp Heynckes in 2013.
That year, he notched 22 goals and 18 assists and finished third in the Ballon d'Or rankings - which he still views as an injustice to this day.
"More than a disappointment. It's the biggest injustice of my career," he told L'Equipe, as per Goal.
"Not only for me, for many people. I was on top and I finished 3rd. I had nothing to envy Ronaldo or Messi that year. I say it in all humility because it is the truth."