The 27-year-old has impressed this season under Steven Gerrard at Ibrox.
He is wanted by a trio of Championship clubs - Leeds, West Brom and Fulham.
Football Insider is reporting the Hammers are entering the race as well.
Goldson is a central defender who can also play in the central midfield and right back.
He has spent time in the lower leagues in England and was a Brighton signing back in 2015.
He joined Rangers last summer and has found his groove in Scotland.