The right-back is now officially available on a free transfer following his release from Barcelona, but he has no plans to retire, as he is still hopeful of making the Brazil squad for the 2022 World Cup.
Alves returned to Barcelona in November 2021 after his contract with Sao Paulo came to an end, and the defender featured on 15 occasions for the club in the second half of the 2021-22 campaign.
The Catalan giants decided against extending his deal, though, with the 39-year-old now seeking pastures new.
According to Goal, Serie A club Athletico Paranaense are currently at the head of the queue for the Brazilian's signature, with their president taking control of the negotiations.
Fluminense are also said to be in the hunt for the South American, while a number of Mexican teams are believed to be keeping a close eye on the developments.
Alves played an important role for Barcelona in the second half of last season, featuring on 15 occasions, including 13 times in La Liga, contributing one goal and three assists.
"I would like to thank all the staff for the opportunity they gave me to return to this club and to be able to wear that wonderful shirt again. You don't know how happy I am," Alves said when confirming his exit.
Meanwhile, he wrote on Instagram: "Now the time of our goodbye has arrived. It has been more than eight years dedicated to this club, these colours and this home... but like everything in life, the years go by, the paths deviate and the stories are written somewhere else at another time.
"I am very grateful to those who decided to give me the opportunity to come back here to be able to say goodbye, but it would not be a goodbye without first thanking everyone behind the spotlight, all of those that ensure that everything is perfect for us, to all of them; THANK YOU."
"I would also like to thank all the staff for the opportunity they gave me to return to this club and to be able to wear that wonderful shirt again. You don't know how happy I am.
"A very beautiful cycle ends and another even more challenging one begins. Let the world never forget: EVEN IF A LION IS 39 YEARS OLD, IT CONTINUES TO BE A GOOD CRAZY LION. Forever, VISCA AL BARCA."
Across two spells, Alves made 406 appearances for Barcelona, contributing 22 goals and 104 assists in the process.
The South American, who has also played for Sevilla, Paris Saint-Germain and Juventus, won six La Liga titles, four Copa del Rey crowns and three Champions League titles during his first spell at the club.
Alves has also won 125 caps for Brazil, captaining his national side against South Korea and Japan in their June friendlies, and he is bidding to make their squad for the 2022 World Cup. body check tags ::