The 38-year-old claimed three Champions League crowns, six La Liga titles and four Copa del Reys during his time at Camp Nou, scoring 21 goals and setting up 101 more in 391 appearances for the club.
Alves - the most decorated player in football history - recently terminated his contract with Sao Paulo after two years in his homeland, and the Brazilian is ready to answer Barcelona's call.
Speaking to Sport, Alves said: "It would sound very opportunistic to say that Barca need me now. I always said that I left because I saw things were not the way I thought they should be.
"You never want to see everything that [has] ended up happening since I left. I've said that when Barca need me and want me, I would be at their disposal regardless of where I am.
"The affection, love and respect I have for this club is too much. If Barca think they need me, they just have to call me. I still think I can contribute anywhere, but more at Barca because of the number of young players that they have now.
"I always look for a club that allows me to compete with the greats, fight for titles and be decisive wherever I am. I want to bring a winning, fighting and conscious mentality wherever I go."
Alves spent eight years with Barcelona before completing a free transfer to Juventus in 2016, and he also spent two years on the books at Paris Saint-Germain before moving to Sao Paulo.