The veteran centre-back is available as a free agent after his short-term contract with Arsenal expired and he is on the lookout for a new club.
Celtic have also shown an interest in the former England international who has now held initial discussions with both the Bhoys and the Black Cats.
Campbell is due to get married in the coming days and Bruce feels his focus will be away from what his football future holds until later in the month.
The former Spurs and Portsmouth defender started last season with Notts County in League Two before abruptly leaving Meadow Lane after just one match.
Gunners boss Arsene Wenger handed him the chance to resurrect his top-flight career at another of his old clubs in January but no new deal was forthcoming at the end of the campaign.
Bruce told Sky Sports News: "We have had a conversation with Sol, I've known the lad a long, long time.
"He's obviously got some decisions to make.
"We've shown him around and shown him what we've got, so we will see what develops over the next 48 hours.
"But I think Sol is getting married next weekend and then is away on honeymoon so I wouldn't have thought there would be much before that happens."