Reo-Coker is available on a free transfer as his contract at Aston Villa has expired.
Bruce is keen to bring in the 27-year-old as he tries to strengthen his midfield this summer.
The Black Cats have also been linked with the likes of David Vaughan, Seb Larsson, Spurs striker Peter Crouch and Sevilla ace Alvaro Negredo.
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The start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.
As always it is the so called “big clubs” that have splashed the most cash in the transfer window so far this summer. Manchester United or City? Arsenal or Tottenham? Who are the winners and losers of the transfer window so far?