Nosworthy still has a year remaining on his Black Cats contract but he has been told by manager Steve Bruce he is surplus to requirements at the Stadium of Light.
The 30-year-old spent last season on loan at Championship club Sheffield United and was keen on a move to Bramall Lane. But the Blades' subsequent relegation to League One ended any interest he had in joining the south Yorkshire club.
Nosworthy's career on Wearside flourished under ex-Sunderland manager Roy Keane after he switched him from full back to centre half, and the Irishman was keen to take his former charge to Portman Road last term. And the former Gillingham man, who has held talks with Reading, Crystal Palace and Ipswich, may still end up there.
Bruce will want to bring in another defender should Nosworthy leave the club and he was linked with a move for Craig Gardener at the weekend.
Gardner, who can play in defence and midfield, was relegated with Birmingham to the Championship on the last day of the season and manager Alex McLeish may have to allow his highly-rated player to leave St Andrews.
City signed Gardner from Aston Villa on a four-and-a-half-year, £3.5m contract. The 24-year-old still has three years remaining on that deal and Birmingham will be looking to claw that fee back should he leave the club.