The two teams went head to head in the Premier League on Monday night, with the Hammers winning 4-2.
Maupay, who did score in the game for his side, was winding up Nolan on the sidelines late in the game.
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Footage showed the two arguing and coming close to a physical altercation, before others got in the way.
While commentating, Manchester United legend Gary Neville had a say on the matter.
He said: "The Brentford striker, apparently, we believe was outside the referees room (at half-time) and Nolan has taken offense to it."