Victory at the Portuguese Grand Prix on Sunday would move the British driver onto 92 race wins, and surpass the German great's mark of 91 that for so long had been considered untouchable.
The pair have struggled in their fourth season together and scored only three points between them in 11 races so far.
Hamilton wins the Eifel Grand Prix on Sunday after Mercedes teammate Valtteri Bottas suffers DNF from the lead.
Bottas set the pace in 1 minute 26.225 seconds, with Lewis Hamilton .136 off his Mercedes teammate in second. Ferrari's Charles Leclerc third fastest, .456 off Bottas, and Sebastian Vettel fifth.
Low cloud and mist made for poor visibility around the Nürburgring track and it was declared unsafe for the medical helicopter to take off before time ran out for the 90-minute session.
Honda is the engine supplier for the Red Bull and AlphaTauri teams. It had resumed competition in F1 in 2015.
3000 fans were present for the first time at the ninth Formula One race this season amid the coronavirus pandemic.
Four-time Formula One champion Sebastian Vettel has signed for Racing Point.
The Alpine F1 team will still use Renault's engines but drivers Fernando Alonso and Esteban Ocon, who is French, will have a car decked out in blue, white and red instead of yellow and black.
The Formula One on Tuesday added four more races to the 2020 calendar, adding that a limited number of fans will be allowed in in a "number of races."
Hamilton's teammate Valtteri Bottas saw his tyre deflate two laps before the finish at the British Grand Prix last week and the same fate awaited the Brit on the final lap.
Bottas took his first pole since the opening race of the pandemic-delayed season in Austria, which he went on to win.
The Mexican driver had hoped to return after spending seven days in quarantine, but his Racing Point team said Friday morning he had tested positive.
Perez became the first Formula One driver to test positive for coronavirus, and it had been unclear whether he would be available to drive after the period of quarantine was extended to 10 days.
Perez was diagnosed with COVID-19 last week that saw him miss the British Grand Prix in Silverstone.
Sergio Perez believes he caught the virus when he travelled to Mexico between the Hungarian and British races to visit his mother after she had an accident.
The revamped Formula 1 season calendar has so far seen three races being completed, all of them were held behind closed doors and the same fate now awaits the Monza GP.
The Algarve International Circuit in Portimao will host the Portuguese Grand Prix on October 23-25, two weeks after the Grand Prix at Germany's Nuerburgring.
Hamilton and others, such as his Mercedes teammate Valtteri Bottas and Ferrari's Sebastian Vettel, took a knee while others appeared to be hurriedly arriving late and not even in position
Canadian billionaire Lawrence Stroll, who owns Racing Point, has reportedly offered Vettel a contract.
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