Latics boss Paul Jewell has revealed that Toffees manager Walter Smith had enquired about the player's availability and that he had held talks with the Northern Ireland international.
The 23-year-old had been a long-term transfer target for Leicester City and was expected to move to Filbert Street, but the deal fell through.
Manchester United and Liverpool have also been linked with the keeper, but Everton are now firm favourites to sign the player.
"Everton do like him, they have asked me about Roy but a chat with Walter is the furthest things have gone at this stage," said Jewell.
Jewell admitted that he would like him to stay at The JJB Stadium, but that it was unlikely he would stay in the Second Division.
"Roy has reported back for pre-season training and is still coming to terms with seeing a dream move to Leicester City and Premiership football break down.
"He's naturally disappointed. I'd have been the same but you just have to get on. Ideally I want him to stay and have told him so."
Everton are thought to be preparing a £1 million offer plus reserve keeper Steve Simonsen for Carroll`s services.
Meanwhile, Wigan striker Simon Haworth looks like snubbing a possible return to Cardiff City.
The Welsh international is a target for Alan Cork's Bluebirds, but Haworth is set to stay with The Latics.
