The 23-year-old former Livingston and Middlesbrough player is a free agent after being released from a short-term contract with Bradford City at the end of last season.
Halliday has been training with Rangers for the past week and has impressed manager Mark Warburton sufficiently to be offered a three-year contract.
A boyhood Rangers supporter, Halliday is now poised to become Warburton’s fifth summer recruit to a revamped first-team squad at Ibrox following the captures of Danny Wilson, Rob Kiernan, Wes Foderingham and Jordan Thompson.
With Rangers’ first competitive action of the season against Hibs at Easter Road in the Petrofac Training Cup just eight days away, Warburton is keen to make further additions.
Wigan Athletic are believed to have turned down a second bid from Rangers for their 23-year-old full-back James Tavernier.
Warburton faces competition for Tavernier, who has a year remaining on his contract at Wigan, from English Championship side Rotherham United.
Rangers also remain interested in former Hearts midfielder Jason Holt who scored in a behind-closed-doors friendly win against Ayr United at Murray Park on Wednesday.
The 22-year-old is understood to be keen on a move to Ibrox but Rangers must first negotiate a compensation fee with Hearts for the player. Holt spent the second half of last season on loan at Sheffield United.