Arsene Wenger will meet with William Gallas' agent next week to discuss the Frenchman's future with the London club.
Gallas is out of contract in the summer and has been linked with a move away from The Emirates with AS Roma boss Claudio Ranieri expressing an interesting in reuniting with the 32-year-old.
Wenger is keen to keep the former captain and is confident he will persuade him to extend his contract when he speaks with his representatives next Thursday.
"It's our desire to keep him here," Wenger said.
"I am not concerned. He is under contract until the 30th of June. We have not found an agreement yet. I meet his agents again next Thursday and we will try to find a solution.
"I would like to keep all that secret. I feel I have to respect both parties and not to come out about the details of negotiations."
As his contract is nearing its end Gallas is free to speak to other teams but Wenger has no idea whether the player has held talks with different clubs.
"I do not know if he has spoken to Roma, but he is out of contract and can talk to whom he wants," added the manager.
"William is speaking to us and our desire is to keep him here.
"I think he wants to stay here."