Should Goss move to Ibrox, he would become Graeme Murty's first signing as Rangers manager.
Midfielder Goss, who moved from Exeter to Manchester United at the age of 16, is currently on the books of Queens Park Rangers, who paid £500,000 for his services a year ago.
The 22-year-old has not made a single appearance for the R's all season, however, and is said to have been informed that he can leave Loftus Road by manager Ian Holloway.
League One Plymouth Argyle were linked with a move for Goss last month (Daily Star) but, according to the Scottish Sun, Rangers are expected to sign him on a deal until the end of the season.
The report does not state whether Rangers' deal for Goss, who is under contract until 2020, would be a permanent or temporary one.
Murty's midfield has been plagued by injuries of late, prompting Rangers to negotiate Andy Halliday's return from a loan spell in Azerbaijan.
Would Goss be a good signing for Rangers?