Bartishvili plays for FC Kolkheti and is expected to secure a move away this summer. Both Arsenal and Juventus have watched him closely over the past year, with the Italians tracking him for at least 12 months.
Arsenal's interest is connected to the arrival of Maurizio Micheli on their recruitment staff earlier in the season. Micheli is regarded as one of football's best talent-spotters and is credited as the scout who unearthed Khvicha Kvaratskhelia, the player to whom Bartishvili is most frequently compared.
Georgia head coach Willy Sagnol spoke about the teenager this month.
"I watched the youth team play — Bartishvili is a very talented player," Sagnol said. "However, for a talented player to take a step forward in his career, technique alone is not enough. The right mindset is needed, and Khvicha Kvaratskhelia is an example of this.
"Hopefully, Andria and the other young players will continue to work and develop to become great players in the future."
Arsenal sporting director Andrea Berta has made youth recruitment a central plank of the club's summer strategy, and the pursuit of Bartishvili sits alongside other targets such as Jeremy Monga of Leicester City as part of a broad drive to reinforce the academy pipeline.
Whether Arsenal or Juventus can ultimately agree terms with Kolkheti and the player's representatives will likely be decided in the coming weeks, with both clubs understood to view Bartishvili as a long-term first-team prospect rather than a pure development signing.
Bartishvili would not be the first Georgian player to use a move engineered by Micheli as a springboard to the top of the game. Kvaratskhelia's rise from a relatively obscure domestic league to Paris Saint-Germain in the space of three years provides the template, and Bartishvili's backers believe his trajectory could follow a similar arc if he lands at the right club.