The Sun says Black Cats boss Steve Bruce has resurrected his interest after the Aussie full-back's move to Atletico Madrid hit the rocks.
Bruce has already shelled out more than £30m on seven new recruits.
But he will ask billionaire backer Ellis Short to dip into his pocket again to fund an 18-month deal worth £3m to free agent Neill, 31.
Bruce needs cover at full-back after selling stand-in skipper Danny Collins and losing George McCartney for up to six weeks with hamstring trouble.
Bruce said: "As a manager I'm going to be judged on my dealings in the transfer market."
Meanwhile, tribalfootball.com understands Neill's move to Atletico was always a non-starter.
Atletico intermediaries insist the Australia captain was never under consideration this week.