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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Being an amiable guy is good for you and Jurgen Klopp is living proof.
Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.