The youngster has already featured for one of the Gers' youth teams and is set to complete a deal in January.
The 19-year-old is set to join the Gers in January, most likely on an academy contract, The Scottish Sun reports, but has already joined up with Mark Warburton's side in the past week.
Leacock-McLeod - who joined the Championship club from Fulham in 2014, having come through the youth system at Craven Cottage - made an immediate impact for Rangers' under-20 side, scoring in a 9-0 victory over Airdrie in a friendly.
The prospect will offer Warburton plenty of versatility, as he is capable of playing on either wing, or in a more central role just behind the striker.
The move is arguably the latest example of Warburton using his knowledge of the English game that he developed while with Brentford, to enhance Rangers' squad. The Ibrox outfit have already brought in the likes of James Tavernier, Gedion Zelalem and Martyn Waghorn from south of the border.
And if Leacock-McLeod can follow in the trio's footsteps, then it will certainly strengthen Rangers' hopes of getting back to the Premiership.