Close turned professional in October 1988, winning his first fight at the Ulster Hall, Belfast, when he knocked out Manchester's Steve Foster in the second of six rounds on a card that included fellow Northern Irish boxers Eamonn Loughran and Sam Storey.
In his seventh bout he beat Rocky McGran to win the vacant Irish Super Middleweight title.
After an October win against Ray Domenge, Close again faced Eubank in a rematch at Belfast's King's Hall.
However shortly before the match the British Boxing Board of Control revoked Close's licence after he failed an MRI scan.
There was some press speculation in 2002 that Close was going to make a return to the ring in an unlicensed boxing event in Belfast, however the fight did not materialise.