The Brazilian right-back hopes to push for a place at the 2022 FIFA World Cup in Qatar but is without a club after leaving Sao Paulo in September.
He would love to make the leap back into LaLiga, in what would be a startling move for a 38-year-old who left Barcelona five years ago.
It remains to be seen whether head coach Ronald Koeman thinks there is a place in his squad for the six-time LaLiga winner.
"I always said that I left because I saw that things were not the way I thought they should be," Alves told Spanish newspaper Sport.
With Joan Laporta back for a new stint as president, Alves believes Barcelona can move in the right direction.
"If left saying that when Barca needed me and wanted me, I would be at their disposal regardless of where I was," he said. "The affection, love and respect that I have for this club is too much. If Barca think they need me, they just have to call. I still think that I can contribute anywhere, but more at Barca because of the number of youngsters they have now.
"In every place I have been, I have always thought that the perfect mix is experience with youth. There will come a time when youth will mature and the older ones will leave. It is a natural cycle, but in football mistakes have been made and this process has accelerated. Processes cannot be sped up. The mix is essential."
Alves played for Juventus and Paris Saint-Germain after leaving Barcelona, winning league titles with both, before returning to club football in his native Brazil.
A three-time UEFA Champions League winner with Barcelona, he joined in 2008 from Sevilla and left eight years later.
In 247 LaLiga games for Barcelona, he helped the team to 95 clean sheets, had 78 goal involvements (64 assists, 14 goals) and created 377 chances.
The latter total across the eight-year period was beaten by only five players, two of whom were Lionel Messi and Cristiano Ronaldo.
Alves said there was a subconscious "thorn" in his mind regarding the FIFA World Cup, and the fact he did not go to the 2018 tournament because of a knee injury.
Winning a gold medal with Brazil at the Tokyo 2020 Olympic Games was rated by Alves as his greatest achievement in the game.
"Many times you stop playing not because of the physical element but because you have been mentally destroyed. And this is one of the things that I have the strongest: I decide when I start and I decide when I finish. And along the way you have to live it intensely, which is what I do," he said. "I know that if I am going to compete in a team, that is what will take me to the [FIFA] World Cup."
He scotched any thought of him lacking the physical wherewithal to compete at the highest level.
"There came a time in Sao Paulo that we played every other day," Alves said. "I am reaping what I have sown all my life, which is respect for the profession, discipline and care that one has to have ... it is what allowed me to compete in the Olympic Games with boys of 18 or 20 years old and have a good performance.
"I don't believe myself to be better than anyone, but I trust my work, my dedication and my preparation to face all my challenges. This is the basis of my entire career."