The 34-year-old has also been romantically linked to actresses Ruth Negga and Gemma Arterton and said they tend to spend a lot of time together while shooting for a film.
"There are parts where for 12 hours on that day you are portraying someone who is so in love that they are on the cusp of insanity - so you can understand that dynamic chemistry," he said.
Cooper said he hates being the subject of public scrutiny because speculation about his personal life were really damaging. "Fame is a difficult thing to be thrown into and I've been burned in the past. The rumour mill can be funny, but unfortunately it can also be really damaging."
Flashback: When sexy models sizzled in bikinis at Tokyo fashion show
Photos: Amy Jackson, Daisy Shah at Mumbai airport
Photos: Sridevi, Irrfan and other celebs at 'Mughal-e-Azam' screening
Photos: WWE Diva Kelly Kelly sizzles in bikinis on Instagram
Photos: Parineeti Chopra celebrates birthday with fans