The Irishman was linked to several moves away from Goodison Park in the summer and is believed to want to be closer to his family in Glasgow.
Reports also claim that Sunderland are prepared to listen to Everton offers for Lamine Kone who was a target of Ronald Koeman in the summer.
Several reports are quoting a fee of around £10m to secure a move for McCarthy to the Stadium of Light this January as Moyes fights for his Premier League survival with the Wearsiders.
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