Gould returned to United last season after spending four years at Kaizer Chiefs, although his time at the Glamour Boys was marred by injury.
Matsatsantsa have already tied up Ronwen Williams with a five-year contract extension and appear eager to see their most prominent stars commit to the club.
Gould's manager Glyn Binkin has confirmed his client's new deal with the Pretoria-based club.
"Morgan had a one-year option. SuperSport have since extended his contract for another season," said Binkin.
The 34-year-old Gould made 24 Absa Premiership starts for SuperSport last term.