Brown, 36 is without a club having being released by Sunderland this summer. He is currently training with Blackburn Rovers but the Yorkshire Post believe that he may strike a deal with the Blades should he fail to earn a contract with the Championship outfit.
Blades boss Chris Wilder has been active in the transfer market, which closes at 11:00PM next Wednesday, and having seen a bid turned down for Millwall's Bryron Webster, a move for free agent Brown could be the ideal solution to solve his defensive worries.