But another candidate could be Daniil Kvyat, who after his departure from Toro Rosso has suddenly turned up in the Montreal paddock.
"I've never been as well as now," the Russian is quoted as saying.
But sources indicate that Kvyat is merely in Canada as Ferrari's reserve driver, while Antonio Giovinazzi prepares for Le Mans.
Yet another candidate is Robert Kubica.
"I have some insider information, let's say it like that," Russian rally driver Aleksey Lukyanuk told SportFM.
"The manager of our team, who helps us with sponsors, used to work with Kubica. He says Robert is sparing no preparation for formula one."
But for now, Hartley says he is unfazed.
"This is the second weekend I've been asked about rumours," he said in Canada. "They're not worth commenting on. You always have them in formula one.
"I have a contract and I know the terms and I know what my speed and my abilities are. In Monaco I was not lucky in qualifying, but overall I had a good weekend.
"I haven't talked to Franz Tost but honestly I'm totally focused on the weekend and don't see the point of discussing what you want to discuss," Hartley added.