The 30-year-old joined the Latics from Club Brugge on a three-year-deal in the summer of 2010 and has gone on to make 77 appearances for the club.
His contract at the DW Stadium expires this summer and so he is available on a free transfer, with Alan Nixon of the Mirror claiming Everton are ready to pounce.
The Toffees are set to offer the former Racing Club defender a two-year contract and bolster the defensive ranks at Goodison Park.
His arrival could speed up the departure of John Heitinga, who has just one year left on his contract and has shown an unwillingness to sign a new one.
Fenerbahce have been linked with Heitinga in the past so if Everton can get £2-3million for the Dutchman and replace him with Alcaraz on a free, that represents decent business in my book.
Heitinga has always been suspect defensively and although Alcaraz doesn't exactly set pulses racing, he was a steady influence in Wigan's back four (was great in the cup final) and would represent decent back up to Phil Jagielka and Sylvain Distin.