The former couple, married for 10 years, announced their split last month, and conflicts over their attitudes towards fame are said to be a possible reason behind it.
"It was a struggle for Chris to have this movie-star lifestyle. He hated the paparazzi attention. They started to realise they didn't have as much in common as they would have liked," contactmusic.com quoted a source as saying.
Another source said: "Gwyneth is someone who likes attention. There is a narcissism there."
The couple has two children together - Apple, nine, and Moses, seven.