The Black Cats parted company with Lee Johnson on Sunday after a shock 6-0 defeat at Bolton left the club outside the automatic promotion places in League One.
Lennon has been out of work since leaving Celtic in February last year in the midst of a failed attempt at landing a 10th Scottish Premiership title in a row, having previously helped land a historic quadruple treble.
Now the Northern Irishman is keen on a return to the dugout and admits the job at Sunderland, who have also been linked with Roy Keane, Grant McCann and Paul Cook, would tempt him.
He told talkSPORT: "It's very appealing I think.
"It has a fantastic fanbase and in a reasonably good position in the league, that would be a job anyone would be interested in.
"But it is so competitive now, the manager's race to get back in or keep your job."