Autosport magazine is reporting that 27-year-old Hartley is the favourite to replace Gasly for the race at the Circuit of Americas track and is in the frame to get a full-time drive at the team next year.
Toro Rosso needs to fill the seat alongside Daniil Kvyat at Austin after it was agreed Pierre Gasly would return to Super Formula to contest the title in the series finale on the same weekend. He is part of a trio including fellow Kiwi Earl Bamber and German Timo Bernhard that leads the World Endurance Championship but will be looking for another drive next year after Porsche's decision to withdraw at the season's end.
Toro Rosso team Principal Franz Tost reportedly wants to use next the race as a chance to evaluate a new driver to add to next year's roster and while Gasly remains a favourite to retain one of the team's cars, the other is now up in the air.
He held the role of Red Bull's reserve driver from 2009-2010 and completed a test for Red Bull in 2008 as well as two for Toro Rosso in 2009 before being dropped from the programme.
In addition, it is also believed he is close to a deal to race for Chip Ganassi in IndyCar next year, meaning there are contractual issues to be ironed out before his Austin appearance can be confirmed.
With enough super licence points to race in Formula 1 Hartley is now contracted to Porsche and competing in the World Endurance Championship, where he could win the title this weekend at Fuji.