Per The Guardian:

The Manchester City defender Wayne Bridge was on his way to Wearside on Tuesday morning as he closed in on a loan move to Sunderland. It is understood that the 31-year-old former England international was due to undergo a medical as Martin O'Neill attempts to bolster his injury-hit squad on the final day of the January transfer window.

UPDATE: The Official site now confirms the move.

UPDATE: Martin O'Neill has spoken about the signing:

"I'm hoping that with Wayne's undoubted experience and ability he can be a big help to the team until the end of the season. "I'm very pleased to have him here and with the number of injuries we've sustained recently I'm sure he'll be a great help to us."

UPDATE: SBNation's Sunderland blog, Roker Report, have their say on the move here.