Britain's world champion, talking ahead of his home grand prix at the weekend, said reports that Verstappen has considered a move to McLaren are "a cool thing" to hear but "not a serious thing".
He added that he and Piastri "are still working very well together".
Reports from media including Sky Sports indicated last week that Verstappen's management had requested, and held, a meeting with McLaren ahead of the Austrian Grand Prix. The content of any discussions was not reported and the Dutch driver has yet to comment.
"It's a cool thing, it's a good thing that a four-time world champion wants to come on board and wants to potentially join the team," Norris said at Silverstone on Thursday as he prepared for the British Grand Prix
"I don't know how much of it's true, but it's a cool thing and if there's an opportunity for me to drive with other people, it's something I've always looked forward to. But it's not a thing for now. It's not a serious thing."
Reports suggested that Verstappen could move to McLaren, swapping seats with Piastri who would head in the opposite direction to Red Bull.
McLaren chief executive Zak Brown said on the Up To Speed podcast released Wednesday that Norris and Piastri are "not going anywhere" and he'd only consider Verstappen if McLaren had an opening.
Besides Verstappen, "quite a few others" in F1 are interested in a potential McLaren drive too, Norris said.
"I'm also just excited for my future with McLaren. I'm still going to be here for many, many more years, so I'm excited for whoever I get partnered with," he added.
"But for the time being, me and Oscar are still working very well together. We're excited to work together for more years too, so that's our focus for now."
Verstappen remains under contract with Red Bull until the end of 2028 but there have been signs the deal includes options to exit earlier under certain conditions.
A planned move to McLaren for his long-time race engineer GianPiero Lambiase increased the speculation of a potential move to McLaren for the Dutchman.
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