HITC Sport understands that the youngster is training with the Robins as they look to thrash out a deal.
The Robins landed striker Shawn McCoulsky from Dulwich Hamlet in the last week, beating a number of Football League clubs to his signature.
Now the Championship club have another youngster in their sights in the shape of Ryan-Khanye.
The 19-year-old was previously with Brentford but was picked up by Erith-Belvedere in the summer, but the left-back has already been attracting interest from a number of League clubs.
HITC Sport understands a number of sides had made approaches for Ryan-Khanye, but he has opted to take up an offer to train with City.
The teenager linked up with the club earlier this week and they are firmly on course to land his signature.
Bristol City are currently sat 21st in the Championship table, four points above the relegation zone.