The 40-year-old French star is in a relationship with fellow actor Guillaume Canet, 43.
"Marion and Guillaume are blissfully happy, and these kind of claims are not what Marion wants to be hearing," a source close to Marion's family in her home city of Paris told Daily Mail.com.
"Claims that she's cheating on Guillaume with Brad will leave her absolutely devastated. This doesn't sound like her at all."
Read more: Why Marion Cotillard has been dragged into the Brad Pitt, Angelina Jolie divorce drama
According to the film's producer, Graham King, Pitt and Cotillard had an immediate connection.
"Brad and Marion immediately had the utmost respect for each other, so once they delved into their characters, their chemistry was electric," he told People Magazine back in August.
"It was crucial for Brad and Marion to not only begin rehearsing together before the shoot, but they also spent a lot of time developing their characters with the director, Robert Zemeckis," he added.
"By the time we got to set, it was really amazing to see these characters already feel lived-in and real."
The pair play a information officer and French Resistance fighter who fall in love. They began filming the movie in England in February this year and also travelled to Casablanca and the Canary Islands for shoots.
Allied is due for release in 2017.