Neymar, 28, has been linked with a return to Barca , nearly three years after joining PSG for a world-record €222 million (£198m/$263m) fee.
But Elber, who starred for Bayern Munich and played 15 games for Brazil during his career, said the Liga giants should opt against taking Neymar back to Camp Nou.
Asked by Cadena SER if Barca should sign Neymar again, Elber said: "No. As he left Barcelona, for me there is no possibility of returning to Barcelona."
Elber added: "For me, Neymar behaved very badly with Barca, because when he wanted to leave Barcelona he said he wanted to be the best in the world.
"I believe that PSG will still not be able to win the Champions League in the next three or four years."
Neymar has won three Ligue 1 titles among numerous domestic trophies since arriving at PSG, the latest coming this season which was declared finished due to the interruption caused by the coronavirus pandemic.
The Ligue 1 giants were into the Champions League quarter-finals when this season was suspended, coming from behind to down Borussia Dortmund in the last 16.
Amid the constant links to Barca, which were also present during last summer's transfer window, Neymar affirmed that he was concentrating on regaining fitness in order to compete in the European competition.
"The aim is to be ready for when they signal the return of club activities, so I can be in the best possible condition," the 28-year-old said.
"I'm here, training hard, with the same rhythm and frequency that I would with the club. Training even harder actually, with more activities to compensate for the lack of games.
"Of course I miss the competition, but fitness coach Ricardo Rosa set up a programme that I have been following to the letter."