The "Nymphomaniac" actress was spotted at the Los Angeles airport on Monday, aceshowbiz.com reported.
Both LaBeouf and Goth, who have been very private about their love life, have not yet addressed the engagement rumours.
Read: Johnny Depp 'cant wait' for marriage
The duo were co-stars in the 2013 two-part drama art film "Nymphomaniac" and have since been romantically linked. Neither of them is shy of showing off their love for each other as they were often caught on camera engaging in public display of affection.
They were last seen together having lunch in Studio City, California on Saturday.
Fans of the star took to social media to share the news of the alleged engagement.
Shia LeBeouf engaged? Girlfriend Mia Goth appears to wearing an #engagement ring at LAX http://t.co/RXVE33QLM7
— BunchesDirect (@bunchesdirect) March 10, 2015
I've been eating nothing but salad and working out meanwhile Shia Labeouf just got engaged to this homeless chick pic.twitter.com/hwiVBS074J
— Old Miami (@flyChy) March 11, 2015
Shia Labeouf is engaged, man I feel old, we been down since Even Stevens
— Jolei (@MsJolei) March 11, 2015
Is Shia LaBeouf engaged ??#Hollywood@HollywoodLife@THR@Deadlinehttp://t.co/z9wKvdytCi pic.twitter.com/Uyd6gRGeYP
— Vishwa Gujarat (@vishwagujarat) March 12, 2015
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