The Mirror says Arsenal have also asked to be kept informed - and could make a late move.
Rodwell, 23, has failed to make an impact at Manchester City and is open to any change of scenery to get his career moving forward again. City are ready to let him go after the midfielder, capped three times by England, made just seven league starts since a £12million move in 2012.
Black Cats boss Gus Poyet hopes to build his side around Rodwell's creative talents.
Roberto Martinez reckons he would quickly return the player to his best back at Everton. For his part, Rodwell is hoping Arsenal manager Arsene Wenger may yet get involved as he would love the chance to remain at a top-four club.
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