Kenny Smith, who according to the New Zealand media source Newshub is Hartley's "mentor", thinks the driver will jump at the chance to race for Toro Rosso next weekend.
After serving as Red Bull's official driver in 2009 and 2010, Hartley was dropped from the junior programme, but had another opportunity in F1 with Mercedes at a young driver test for Mercedes in 2012.
Brendon Hartley is Toro Rosso's new driver and will make his F1 debut in Austin next weekend.
Autosport magazine has reported that Hartley, 27, is the favourite to replace Pierre Gasly for the race at the Circuit of Americas track and could even take over as team driver in 2018. I want to say a huge thanks to Red Bull for making this a reality, and to Porsche for allowing me to do this alongside the World Endurance Championship.
It's also believed Hartley was close to a deal to race IndyCars alongside fellow New Zealander and four-time series champion Scott Dixon at Chip Ganassi Racing.
Ronald Koeman not interested in Holland job
We need to win and we need to change our situation in the table and that starts this Sunday. "Let's hope he will be totally fit". I'm not interested in his comments.
However, acquiring the Kiwi will require some ironing out by the Italian Formula 1 team - the 27-year-old is now contracted to Porsche in the World Endurance Championship - a competition he could win this weekend with a solid performance in Fuji.
Toro Rosso have another standby option in former driver Sebastien Buemi, who has won the Formula E electric title since he last competed in Formula One in 2011.
Brendon Hartley, 26, returns home after winning endurance championship alongside Porsche teammates Mark Webber and Timo Bernhard.
"He'd have to go to formula one because that has been his main aim from his early days, and what he has been aiming for", Smith said.
"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".
"He is a wonderful kid and It has been so good to associated with him over the years".