The 31-year-old has spent his entire career at the Nou Camp but announced in January that he would not be signing a new deal.
His contract does not expire until 2014 but was expected to leave this summer, with Barca in turn linked with a host of replacements.
Rosell, however, has revealed boss Tito Vilanova and director of football Andoni Zubizarreta are hopeful the player will stay for another season, even if that means the club risk losing him on a free transfer next summer.
"I want to speak with the player," he said. "Tito, Zubizarreta and I would like a direct meeting.
"The player does not have to leave the club in the summer as his deal ends in 2014. After that we will analyse the goalkeeping situation."
Rosell also played down talk of a summer move for Santos' Brazilian superstar Neymar, who has been heavily linked with a switch to the Nou Camp.
"Many clubs are interested but Neymar is still a player of Santos," he added.