The Sun reports that Hamilton and Mercedes boss Totto Wolff are "disillusioned" with the sport following the controversial outcome of Sunday's race.
He said: "Lewis and I are disillusioned at the moment. We are not disillusioned with the sport - we love the sport with every bone in our body and we love it because the stopwatch never lies.
"But if we break that fundamental principle of sporting fairness and authenticity, then suddenly the stopwatch doesn't become relevant anymore because we are exposed to random decision-making, it is clear you may fall out of love with it."
Reports that Hamilton may quit the sport follows on from the news that Mercedes have dropped their appeals against Verstappen's victory, but the result could have a much bigger impact in losing one of F1's most high-profile stars.
Hamilton and Wolff are also both expected to snub the FIA's gala prize giving ceremony in Paris, despite incurring a hefty fine in the process.
The Brit may still continue in the sport, with his current contract at Mercedes running until 2023, and Wolff hopes that contract will be honoured.
"I would very much hope that Lewis continues racing because he's the greatest driver of all time. We will be working through the events over the next weeks and months.
"I think as a racer his heart will say 'I need to continue' because he's at the peak of his game, but we have to overcome the pain that was caused on Sunday, also because he is a man with clear values and it's difficult to understand that that happened."
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