That could change within the next fortnight with Hartley, a previous victor of Le Mans 24, shaping as the strongest contender for the vacant Toro Rosso seat at next week's US Grand Prix.
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.
With current driver, and main point's scorer Carlos Sainz Jr. making an early move to the Renault Sport Formula 1 Team for the next race in Austin, Kvyat was already set to return to Toro Rosso at the next round of the season.
Brendon Hartley could be poised to become the first New Zealand Formula 1 driver for more than three decades.
Hartley, the Red Bull official reserve driver in 2009 and 2010, completed one test for the team in 2008 and two for Toro Rosso in 2009 before being dropped from the team's junior programme.
Hartley was formerly part of the Red Bull Junior Team and has enough Super License points to compete in Formula One; but he is also now contracted to Porsche in the World Endurance Championship (WEC) and is purportedly in talks with Chip Ganassi for a 2018 IndyCar deal.
Brendon Hartley is Toro Rosso's new driver and will make his F1 debut in Austin next weekend.
Hartley is contracted to Porsche in the World Endurance Championship (WEC).
"I could see that when he was 12 years old driving Formula Vees, driving off the track and doing all sorts of insane things, he tried so hard - and Brendon never gave in".
"There is always time to go back to Indycars because he is still young". It is a dream come true for a Kiwi to do what he is doing.
"Brendon is coming as the reigning 24h Le Mans victor and he's also leading the current FIA LMP1 World Endurance Championship, which he won in 2015 as well", said Tost.
"We are really happy to have him back in our team".