Sightings of them together have been few and far between since last year, reports the Mail on Sunday. In February they attended a BAFTA party in Britain thrown by Miramax mogul Harvey Weinstein.
Uma and her millionaire beau have been together since 2007
A few weeks ago the couple were due to attend a gala together in the Big Apple - but Arki, as he's known to friends, didn't turn out. Meanwhile, the silver screen beauty appeared not to be wearing her engagement ring.
Uma and the French hedge fund tycoon, who is worth an estimated $200 million, have had a break before. In 2009, she gave him back his eight-carat sparkler, but the split was short lived and the lovers were back in each other's arms a few months later.
For years they've been juggling family commitments in different parts of the world. In July 2012, Uma gave birth to their daughter Rosalind Arusha Arkadina Altalune Florence, known as Luna for short.
She is also mother to 14-year-old Maya and Levon, 10, from her marriage to Ethan Hawke. Speaking about her ties to the Big Apple, she said: "We can't live anywhere else because my children's father lives here."
They live on opposite sides of the Atlantic due to family commitments
Arki, 51, also has two sons - Flynn, 16, and Aurelius Cy, 10 - from his relationship with Elle Macpherson. To complicate matters further, the Australian supermodel recently married Miami-based property mogul Jeffrey Soffer, who has three children of his own.
In her most recent interviews Uma gave no hint that there were any problems in her personal life. "I'm happier now than I've been in many, many years," she has said. "I'm trying to live as peaceful a personal life as possible."