The Brazilian arrived during January`s transfer window and the Portuguese side are happy with how he has adapted.
The player`s agent Roberto Assuncao has yet to talk with both clubs about the possibility of extending his stay, but admitted the player is happy in Portugal.
Assuncao said: "I have not yet received a call from the clubs, but I expect to travel soon and solve the subject quickly.
"He is willing to continue for a season more, albeit with better conditions."
Geovanni is contracted to Barca until June 2006, and a potential problem facing Benfica is that they would have to pay 40 percent of the player`s contract.
It has been rumoured that if Benfica fail to land the midfielder, Celta Vigo may step in.