The rumours emerged as she walked the runway at the Victoria's Secret Fashion Show in Paris, France on 30 November(16), where shielding her stomach from full view with a tan trench coat and a short, red fringed robe.
Representatives for Irina and Bradley have done little to calm the baby fever by refusing to issue a denial, and now gossip mongers believe the couple may also be planning to wed after the model was photographed wearing what appears to be an engagement ring on her left hand while out in Los Angeles this week (begs12Dec16).
In the paparazzi pictures, the Russian beauty sports a loose-fitting black mini-dress and sunglasses, and is jewellery free except for an emerald and diamond sparkler on her left ring finger. She is also shown holding her handbag close to her body, seemingly trying to hide any hint of a baby bump from the cameras.
The famously private couple has yet to comment on the latest rumours surrounding its relationship.
The Hangover star has been dating Irina, 30, since the spring of 2015, and they went public with their romance in April, 2015, when they were spotted on a Broadway date in New York City.
They made their official red carpet debut as a couple at the L'Oreal Red Obsession Party in March (16), when Bradley accompanied Irina to the Paris Fashion Week event.
If the engagement news is true and the couple go on to wed, it will be Bradley's second marriage. The 41-year-old was previously wed to actress Jennifer Esposito for less than a year, while his exes also include his Guardians of the Galaxy co-star Zoe Saldana and British model Suki Waterhouse.
Meanwhile, Irina romanced Portuguese soccer stud Cristiano Ronaldo for five years until the start of 2015.