Speaking at the launch of Mercedes' new W09 car at Silverstone, Hamilton said that he had already made it clear to his current Formula One team that he is not considering any other options outside Mercedes.
Brown insisted that McLaren and almost all other teams would be very interested to rope in Hamilton.
The four-time F1 champion was heavily criticized after he posted a video on his Instagram account wherein he could be seen lambasting his nephew online and making inappropriate comments on his relative's choice of Christmas attire.
Hamilton who holds the record for highest pole positions (72) said he was assured from the beginning of doing well in the 2017 season.
Describing Bottas as an "amazing" teammate, Hamilton backed the former to put up a more sustained challenge next season.
Mercedes driver Lewis Hamilton recently became a four-time world champion with a ninth-place finish at the Mexican Grand Prix, the race which was won by the Red Bull's Verstappen.
The 30-year-old German finished behind Mercedes-Amg driver Lewis Hamilton in the 2017 F1 driver standings.
The Brit driver won the F1 championship by a margin of 46 points over Vettel whose campaign imploded with crashes and reliability issues and resulted in a series of poor results in Singapore, Malaysia and Japan.
Lewis Hamilton has won the F1 title in three of the past four seasons with Mercedes, losing out to former teammate Nico Rosberg last year.
Despite Vettel leading the title chase for the first half of the Formula One championship, it was Hamilton who eventually took his fourth drivers' championship title.
Hamilton's winning margin of 46 points over Vettel does not reflect an often tense title battle, one in which Ferrari had a genuine chance of breaking Mercedes' stranglehold until Vettel's alarming dip.
Hamilton, who won nine races in the 2017 season to secure the title, failed to clinch the top podium finish in the Brazilian and Abu Dhabi Grand Prix.
The Finnish driver comfortably secured the third win of his F1 career, all coming this season since joining from Williams.
The Briton raced to the top of the leaderboard late in the sun-drenched afternoon session, placing 0.273 seconds ahead of Mercedes teammate Valtteri Bottas.
Vettel was .149 seconds behind Hamilton, and Red Bull driver Daniel Ricciardo was .303 back in third.
Vettel won the last race in Brazil, but Hamilton clinched his fourth Formula One title — and third with Mercedes — the race before and faces no pressure in the season finale.
With Hamilton wrapping up this year's title two races ago, the pressure is off this week at the season-ending Abu Dhabi Grand Prix.
The former team-mates were good friends in their early racing day, but fierce inter-team competition at Mercedes resulted in their fallout.
Vettel started second on the grid, but overtook pole sitter Valtteri Bottas of Mercedes on the first lap and then led most of the way.
Hamilton, who won his fourth F1 championship in the Mexico GP, walked away from the crash without injury and will start at the back of the grid on Sunday.
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