Carew has been linked with moves to both Manchester City and Tottenham in recent weeks.
O’Neill told the Daily Star Sunday: “We want John to stay at the club – he’s signed for a couple of years and we and we want him to stick around.
“He’s very popular with the crowd and that helps his confidence. And his goalscoring ratio is now up where it should be.
“We want him to stay here, it’s a simple as that.”