"Timothée’s schedule is grueling, with very little downtime," a source tells PEOPLE of the 'Dune: Messiah' actor

The "Kardashians" star and the "Dune" actor reportedly "haven't seen each other" in weeks due to their "grueling" schedules.

While the pair hasn't been spotted together over the past weeks, Chalamet returned to social media to promote his new project, the movie "Marty Supreme."  He shared the movie's trailer on his Instagram,