The comedian, who filed for divorce from Perry in December 2011 after only 14 months of marriage, is said to have become upset after seeing photos of the 'Part of Me' singer at Coachella last month with Robert Ackroyd of Florence + the Machine.
According to Grazia, Brand has admitted that he "gave up" on his relationship with Perry too quickly and believes that splitting was a "mistake".
"Word has it Russell was 'seething with jealousy' when he saw pictures of her with Rob. He apparently feels he gave up on their relationship too easily," a source told the publication.
"It's fair to say that Russell only wishes Katy happiness but perhaps he should have realised just how special his wife was when he was married to her rather than five months later."
Last weekend, Brand lost his temper during a stand-up show in Atlantic City, New Jersey with a heckler who repeatedly called out Perry's name from the audience.
Brand was recently linked to David Hasselhoff's ex-girlfriend, Playboy model Anouska de Georgiou.
Watch Katy Perry's video for 'Part of Me' below: