Maupay took to social media following the 1-1 draw on Saturday to highlight an off-the-ball tussle with United midfielder Scott McTominay.
Referee Simon Hopper booked both players for the incident and Maupay took to social media to mock the midfielder.
The Frenchman wrote on X: "This fan was desperate for my shirt."
Man United fan Littler responded to an article covering Maupay's post by writing on Instagram: "Talks more than he scores."
Maupay, 27, with eight goals in 30 games this season, did not let the post go and retaliated. The Brentford forward used a clip of the 17-year-old world championship runner-up reeling in the 'Big Fish' - a 170 check out in darts - in celebration during a recent Premier League darts match.
"Talk about a big fish," Maupay wrote, adding laughing emojis and a fishing rod.
The unexpected exchange is the latest in a series of incidents involving Maupay, who has wound up players and fans of rival clubs.
Luke Littler responded to Neal Maupay's latest wind-up comment after Brentford's clash with Man United last night
It comes after Maupay joked Scott McTominay was a 'fan desperate for my shirt' with a photo of the Scottish midfielder holding his shirt pic.twitter.com/Iq6VKp59ov
- SPORTbible (@sportbible) March 31, 2024 Maupay had previously used a darts celebration to get Tottenham players worked up, with the Frenchman using James Maddison's signature darts move after scoring against Spurs.
Tottenham went on to win 3-2.
"Apparently, you're not allowed to throw a dart because it's only him [Maddison] that can do it, the way he got offended. It was quite funny," Maupay said after the incident.
"The only thing is, it would have been even better if we'd won. But we lost in the end.
"Just by throwing a dart, I got 11 players on toast. It was so easy."
Maddison told TNT Sports: "He's not scored enough goals of his own to have his own celebration, so he's copied mine."
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Maddison's comments irked Maupay, who responded on Instagram after the game, mocking his opponent's relegation with Leicester last season.
The Frenchman wrote: "Gutted we couldn't get the win. More goals and less relegations in my career than James Maddison."
Just days later, Maupay clashed with Manchester City's Kyle Walker when he was accused of making comments about the defender's children.
The forward was slammed for his actions but has insisted he has never crossed a line, denying the allegations around his supposed comments to Walker in his side's 3-1 defeat to the champions in February.
While Maupay's recent inflammatory actions have largely ended in his team's defeat, his latest post came after the Bees fought back against Man United to earn a valuable point.
Thomas Frank's men earned a 1-1 draw through Kristoffer Ajer's 99th-minute strike that cancelled out Mason Mount's goal three minutes earlier.