The point guard, who missed the start of last season while recovering from an ACL tear, is heading into the final year of his contract with the team.
Grousbeck told ESPN: "It's my goal to keep Rondo here. I think we all want that. And I actually honestly think, he should speak for himself, I think Rajon wants to stay, or would be very happy to stay.
"We'll see how this season goes, and how the negotiations go, but he's proud to be a Celtic. I know that. He's proud to wear that [2008 title] ring and he deserved it."
Rondo featured in 30 games last season, averaging 11.7 points for the Celtics.