Campbell has also been in talks with Celtic and Arsenal
Veteran defender Sol Campbell held talks with Sunderland on Thursday over a possible deal with the Premier League side, BBC Sport understands.
The 35-year-old defender is out of contract after playing for Arsenal in the second half of last season.
In June he held talks with Celtic over a possible switch to the Scottish side.
"I have to talk to Arsenal as well because they are still at the table. I have to talk to everybody," said Campbell after speaking to Celtic.
"But the main thing for me right now is my wedding and honeymoon. I don't think I'll be committing myself to any club until after that."
Campbell left his boyhood club Tottenham to spend five years with Arsenal between 2001 and 2006 before moving to Portsmouth, returning for a second spell with the Gunners last January on a short-term deal.
Sunderland recently signed 22-year-old ENPPI defender Ahmed Al-Muhyammadi on a season-long loan and Argentina international full-back Marcos Angeleri has been training with the club.
Celtic boss Neil Lennon has recalled Stephen McManus from Middlesbrough and, if Campbell did sign for Celtic, he would join Dutch pair Glenn Loovens and Jos Hooiveld, Norwegian Thomas Rogne and Irishman Darren O'Dea in competing for a starting place.
Campbell would bring a wealth of experience to any back-line, however, having played 73 times for England and made almost 500 appearances for Tottenham, Arsenal and Portsmouth.
The former international may yet be offered a one-year deal to stay at the Emirates after impressing in his 14 appearances since returning to London.
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