Bradley Cooper and Irina Shayk were ''living totally separate lives'' before their split.

The 33-year-old supermodel reportedly decided to end her relationship with the 'A Star is Born' star - with whom she has two-year-old daughter Lea De Seine - at the end of last month because the pair rarely spent any time together.

A source told PEOPLE: ''[Irina is] not focused on the celebrity part, or on the fame -- she just wants to protect her family. Bradley is very into work and is trying to take advantage of every career opportunity right now. They spent a lot of time apart.

''They were living totally separate lives. If he was in L.A., she's out of town, and if she was in town, he was out of town.''

It has also been reported that the pair tried to save their four-year relationship, for the sake of their young daughter but that they failed to ''make a life together outside of the child''.

A source told the New York Post's Page Six: ''They never shopped for their own house in California. It was just his house. There were no moves in that direction. Then there's the fact that they never got married after they had a kid. She was certain that would happen. It felt like they weren't truly making a life together outside of the child.''

Bradley and Irina are said to be working out the terms of their split, with the actor likely to let Irina keep his Los Angeles home as ''her place in the West Village is too small at this point for a child''.

The insider added: ''He wants to part on good terms, or as good as it can be in this situation.''