The 25-year-old has struggled to earn regular gametime in the Premier League this season, having turned out on just seven occasions, after getting back into the squad following life-saving heart surgery.
It’s understood that Brighton are willing to listen to offers for the centre-back and Rangers are hoping to lure him north of the border.
Incoming Rangers boss Steven Gerrard is keen to strengthen at the back and feels Goldson could help provide some stability.
Reports claim Rangers will make contact once the transfer window opens, however, they aren’t prepared to part with a big fee for his services.
Bayer Leverkusen have signed keeper Lukas Hradecky from Eintracht Frankfurt ahead of Bernd Leno's likely exit.