The 21-year-old enjoyed a fine spell on loan at Oldham Athletic last season and Gerrard is keen on bringing him to Ibrox with Josh Windass expected to leave.
Bryan is predominantly a left-sided centre back but can also play defensive midfielder, as Gerrard is keen on adding depth to his midfield.
It is reported that Rangers are interested in the permanent signing of Bryan, with a deal believed to be worth £2.5 million having been agreed between the clubs.
The 'Daily Mail' are reporting that Bryan is discussing personal terms at Ibrox, as he is poised to sign a three-year deal with the club.
If the deal goes through Kean Bryan will be Rangers' 11th summer-signing, with the likes of Connor Goldson, Nikola Katic, Ryan Kent and Jon Flanagan having already joined the club.