The Daily Record claims the Ibrox side are weighing up a move for the centre back to provide cover and competition to Connor Goldson and Niko Katic.
But Forest’s Championship rivals Aston Villa are monitoring the player’s situation, while Stoke City and West Brom are also keeping tabs on the 21-year-old.
Worrall is some way down the pecking order under Aitor Karanka and the City Ground club are thought to be happy for him to head out on loan.
He had a temporary spell with Dagenham and Redbridge during the 2015/16 season, playing 15 times and scoring once.
Since coming up through the ranks at Forest he has made 56 appearances in red and white, with one goal to his name so far.
The 6ft 4in central defender captained England to victory in the 2017 Toulon Tournament, alongside former Hearts loanee Demetri Mitchell.
The Forest defender was voted “second best player” of the competition, behind team mate David Brooks, and was named in the best XI of the tournament.