Neymar, 27, could reportedly head back to Camp Nou just two years after leaving the La Liga giants for PSG.
According to Globo Esporte , Barca may pay €100 million (£90m/$112m) and give PSG players to bring Neymar back to the club where he previously spent four seasons.
The players in contention are reportedly Samuel Umtiti, Ousmane Dembele or Ivan Rakitic.
Tite is without the forward at the Copa America due to an ankle injury, with Neymar missing the entire tournament after picking up a knock against Qatar in a pre-tournament friendly.
Despite the PSG star's absence, Tite urged Neymar to go where he felt happiest in the wake of the recent rumours.
"I would go to a team where I always felt happy – as a person, as a human being and as a family, because there I will be professionally better," he told a news conference.
"They are very particular situations. It is a professional issue. It has to do with where you feel good, where you feel happy."
Without Neymar, Brazil opened their Copa America campaign by beating Bolivia 3-0 in Group A.
Philippe Coutinho stepped up with a pair of goals for the host nation, with Everton providing Brazil's third in the tournament-opening victory.
Prior to the tournament, veteran defender Thiago Silva pointed to Coutinho as a player that would need to step up in Neymar's absence, while the likes of Richarlison, Roberto Firmino, Gabriel Jesus and David Neres will be looked at as vital goalscorers.
The front three of Richarlison, Neres and Firmino started in the win over Bolivia with Coutinho in an attacking role just behind them.
Ahead of facing Venezuela in Salvador on Tuesday, Tite was giving nothing away about his team's approach.
"The biggest meaning and the most important thing is not to give opportunities to give the opponent an idea about how we are going to play," he said.
"We don't want to make it easier for the opponent, since the players know who will play."
After facing Venezuela, Brazil will face Peru in their final group game on Saturday.