Norris is set to start his sixth season with McLaren while Australian Piastri had a strong debut last year after a legal tussle for his services with Renault-owned Alpine in 2022.
Champions Red Bull have made no secret of their interest in Norris, whose contract at McLaren expires at the end of 2025 with the sport entering a new engine era and general reset in 2026.
"We have Lando under contract for another couple of years, of course we are in dialogue with him on a continuous basis," Brown told reporters at a livery launch at the team's Woking headquarters.
"We’re very focused now here obviously on the short term, but 2026 is not far away and we recognise that being able to retain Lando and Oscar for the foreseeable future is definitely a key element and something that is a high priority for us."
Piastri has a contract to the end of 2026.
Brown said his approach was to take care of all his employees, sponsors and drivers so that they wanted to be part of McLaren.
"I tend to focus on making sure McLaren’s the best environment and people want to be with us because you ultimately cannot control external approaches to those various people," he explained.
"I’m very confident in the relationship that we have with Lando, I know he’s very excited for this year and was very impressed with what he saw in the second half of last year.
"He loves working with (team principal) Andrea (Stella) and everyone on the team, so all we need to keep doing is keep giving him the environment that he wants to be in and then I’m confident he’ll stick around."
Stella said Norris, who had six second places and a third last year and now jointly holds the record for most podiums without a win (13), brought a lot to the team.
"The relationship between Lando and Oscar I think is a point of strength for our team," he said. "The two have almost complimentary driver characteristics from a driving and technical point of view.
"For Lando it’s almost unexplored as to how good he is, sometimes he surprises us with some of the performances he can put together."
