McLaren announced on Wednesday that Norris had signed a new four-year deal taking him to the end of the 2025 season, securing his long-term future.
Norris only signed his most recent contract last May, but was rewarded for his breakout season in 2021 that saw him score four podiums and his maiden F1 pole position.
The deal locks Norris in with McLaren for a deal that both sides hailed as being an important source of stability, but also fends off any interest from rivals in signing Norris.
Asked if he had any interest from rival teams, Norris said: "There were little chats here and there. But that's all, and nothing went far.
"As soon as something came up, that's when I would continue to go to Andreas [Seidl] and have a conversation about what our future holds and so on.
"There were little things, [there's] no point lying about it, here and there with various other teams, but nothing that went far at all."
Norris wouldn't be drawn on which teams had made an approach to him, but said "you'd probably be able to guess reasonably well".
Team principal Andreas Seidl said he was "not aware of any teams speaking to me about getting Lando", but explained the fresh contract was an important step to aid McLaren's long-term planning.
"With the announcement last year, it was just an extension of an existing contract which brought us only to two more years with Lando," Seidl said.
"If you look at the overall plan we have in place here, the journey we are on, we know that despite the good steps that we made in previous years, we have big next steps to make.
"We also know that after all of our organisational changes we did here at McLaren, the cultural changes, that's the plan we have in place on the infrastructure side, we simply need more time in order to keep growing as a team and to finish this infrastructure projects and actually benefit from them.
"In order to achieve these ambitious targets we are having, to get back to the position where we fight for race wins every weekend, having Lando with us and having this consistency and continuity in the driver line-up will be an absolute key to achieve these targets or these objectives.
"Of course, it's very important to lock in Lando with us in the end of '25."