The 22-year-old met with officials from the Portuguese giants in Lisbon airport on his way back from a holiday in Brazil and is keen on the move.
Geovanni linked up with his agent, Roberto Asuncion, to hear Benfica's proposal and will meet with Barca officials next week.
"The first I heard about Benfica's interest was on Tuesday, but only after meeting them do we know that they are serious," said Asuncion.
"When he arrives back in Barcelona we will know if the deal is possible because we have to speak to them first."
Barca coach Louis van Gaal is desperate to bring in some fresh faces and is keen on Ajax captain Cristian Chivu, but with Geovanni at Camp Nou the club's quota of non-EU players is full.
The deal will see Geovanni join Jose Antonio Camacho's team until the end of the season and he will link-up again with former Barca midfielder Simao.
