O'Neill is desperate for 24-year-old Cattermole to sign a new contract to stop him leaving for free next summer.
He said: "I would like him to stay and I have never wavered from that.
"He is in his final year of his contract and is in a decent bargaining position.
"He did well in the games he played last season. He missed as many as he played, through one reason or another - generally suspension.
"Overall, I am pleased with him and I would like him to stay. I'm hoping he feels the same. I can't have this conversation with the player every single day. At some stage I hope he is made an offer where he wants to stay."