Team boss Franz Tost gave a strong hint on Radio Sport on Sunday that Hartley would get another crack in Mexico and his strong first-up showing should only further enhance that.
Hartley was pleased with his overall performance in Austin.
"It was tough out there, but it's been an awesome debut Grand Prix," he said. "It's all starting to sink in now and it won't be until I go to bed and put my eyes at rest that I'll start to process everything."
He started the race in 19th after the team changed out his power unit and accepted a grid penalty as a result. After a cautious start, he got better as the race went on.
"I didn't do the best of standing starts, but it's been a long time since I did one of those," the current World Endurance Championship leader said.
"After that, I was in many battles and I'm satisfied with my race - the pace was pretty strong, especially at the end. I think the only small mistake I made was getting overtaken by [Lance] Stroll a quarter into the race, as I couldn't pass him back and he held me up a bit.
"So there's been lots of challenges, lots of things to learn and I hope I get another shot at it to put all these experiences into practice.
"I've enjoyed every single moment of this race weekend and I'd like to thank the whole team for this, it's been amazing."
Toro Rosso are expected to make a call on which two drivers will get behind the wheel in Mexico today but they were certainly pleased with the Kiwi's debut.
"Brendon should be pleased with his race, as he has performed consistently and delivered on everything we asked of him. For sure he picked up useful experience and understanding of our car. Well done to him," Head of Vehicle Performance Jody Egginton said.
