Sullivan has previously stated that Scott Parker was the only West Ham player that was not for sale.
“I hope [Robert] does have a long-term future at West Ham,” Sullivan told The Guardian.
“We’ve got a fantastic new goalkeeping coach [David Coles, who has joined from Portsmouth] who I think will improve him dramatically.
“You’re never too old to learn and I think he’ll learn a lot.”
Green still has two-years left on his contract with the Hammers.
“All the players with two years to go – we will look at them in January, when there is 18 months to go,” said Sullivan.
“We will see how they’re playing and how the club is doing and we’ll see what offers we can put to them.”