Carroll, 29, is understood to have been sent home from West Ham United training yesterday by boss Moyes, who was unhappy with the player's attitude on the bench during their defeat against Manchester City.
Gateshead-born Carroll left Newcastle for Liverpool in a record £35million deal seven years ago, and has often been tipped to return to Tyneside.
BetStars Director of Trading Ian Marmion said: “Andy Carroll’s West Ham future is up in the air following a training ground bust-up with manager David Moyes and the Geordie is now primed for a summer exit.
“Carroll’s boyhood club Newcastle United are the 3/1 favourites to bring the 29-year-old back to his hometown this summer after selling him to Liverpool back in 2011. Chelsea were heavily linked with the lofty striker in the January transfer window and the Blues are now valued at 9/2 to sign the target man this time around.
“Meanwhile, Everton are looking to bolster their attacking options this summer and the Toffees are valued at 8/1 to bring the England international to Merseyside, while Manchester United can be backed at 14/1 to make a shock swoop for the Hammers’ frontman.”