HITC Sport understands that the forward has been training with the Robins and is ready to sign a professional contract.
The teenage striker spent last season with Dulwich Hamlet, and attracted interest from a number of Football League clubs with his performances.
However, HITC Sport understands that Bristol City have now lined up a move for the talented target-man - who is ready to sign a professional contract at Ashton Gate.
McCoulsky has been training with the Robins and they are ready to push through a deal in the coming days.
Steve Cotterill is in the market for fresh faces and added firepower, with his side currently sitting bottom of the Championship table with seven points taken from their opening 10 games of the season.