The 29-year-old defender crumpled to the Ibrox turf in agony after taking the ball off Liverpool forward Darwin Nunez in the first-half of the 7-1 defeat by the English Premier League outfit.
Goldson was immediately replaced by Leon King and was then spotted leaving the stadium on crutches.
The Daily Record reports that the former Brighton man has suffered a suspected thigh muscle tear, which would leave the player facing a prolonged spell out of the team.
Rangers already have injury concerns in central defence, with Filip Helander and John Souttar currently on the treatment table.
Midfielder Ryan Jack also left the pitch early due to a calf knock and he will be a doubt for Rangers’ cinch Premiership match against Motherwell at Fir Park on Sunday lunchtime.