The Sun says the left-winger turned down a new three-year deal to stay with the Gunners in the summer.
But he has decided to look elsewhere and is hoping to impress Rangers boss Gerrard in Scotland.
Tormey featured prominently at Under-23s for Arsenal last season.
The talented 20-year-old scored four goals in 15 appearances.
And he also played four times in the EFL Trophy.
He battled back from a serious knee injury but players such as Bukayo Saka moved ahead of him in the Arsenal pecking order.