Norris, 18, is leading the Formula Two championship and seen by former world champions McLaren as a bright prospect for the future.
"I'm flattered by the stories but I'm focused on F2 and committed to McLaren," said the teenager. "I leave this sort of thing to my management."
Reports emerged in Italy after the Monaco Grand Prix that Toro Rosso, who last year loaned their Spanish driver Carlos Sainz to Renault, had Norris in their sights as a possible replacement for Hartley.
The Kiwi, who won the Le Mans 24 Hours and World Endurance (WEC) title with Porsche last year, made his Formula One debut late last season but has made mistakes and under-performed compared to French team mate Pierre Gasly.
The BBC reported that the Toro Rosso approach had been rejected.
"We are not surprised that other teams approach our drivers. They clearly believe they are as talented as we do," a McLaren spokesman was quoted as saying.
McLaren and Toro Rosso team members were travelling to Montreal for this weekend's Canadian Grand Prix and not immediately available for comment.
Norris would be in line to replace either two times world champion Fernando Alonso or Belgian Stoffel Vandoorne at McLaren if the former decides to leave Formula One or the latter is dropped at the end of the year.
Vandoorne has struggled to match Alonso, who is now 36 and also committed to competing in the WEC with Toyota.
The Spaniard wants to win the 'Triple Crown' of the Indianapolis 500, Le Mans and Formula One's Monaco Grand Prix/world championship and is competing at the French track this month.
McLaren are also considering setting up an Indycar team, which could take Alonso back to Indianapolis.
The BBC quoted "one source close to the situation" as saying McLaren had an October deadline to offer Norris a full-time race seat or leave him free to join another team for the last two races.
(Reporting by Alan Baldwin, editing by Toby Davis)
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