Hollywood hunk Bradley, 40, and 23-year-old model Suki, who were first linked together in March 2013, are thought to have parted ways two months ago.
People report that Bradley and Suki ended their romance before the Oscar Awards in January.
A source told the US publication that they have remained friends despite their split.
Suki's rep declined to comment, while Bradley's rep could not be reached for comment.
Bradley and Suki first sparked romance rumours in 2013 after they were spotted looking cosy on set in Boston. However, the pair largely kept their romance under wraps.
In an Elle U.K. interview in December 2013, Suki revealed that Bradley caught her eye at the Elle Style Awards in February 2013.
"I'm not one of those girls who goes on about their boyfriends," she said. "I do think whatever I say will sound weird. But the truth is, if I start talking about him, I probably won't be able to stop. And I don't really want to talk about him, you know?"
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