Sunderland have had a bid for Norwich City goalkeeper John Ruddy rejected but talks are ongoing.
The 29-year-old has made over 200 appearances for the Canaries and will only move if the two clubs can agree on a fee.
Moyes was linked with a move for Manchester City's Joe Hart but the goalkeeper chose to join Italian club Torino on a season-long loan.
Sunderland were forced to play England under-21 international Jordan Pickford in goal for the Premier League away draw against Southampton last weekend due to No 1 stopper Vito Mannone suffering a fractured elbow.