Paltrow and Martin announced their separation in 2014 after 11 years of marriage.
Notwithstanding their split, the two have repeatedly been spotted spending time together with their children Apple and Moses. The foursome were spotted having vacation together as a family last week on a spring break getaway in Mexico, reported People magazine.
"They are both very private and very aware that who they date attracts attention. They want to make sure, as their kids are still in elementary school and become aware of their celebrity, that they are not exposed to things that might be hurtful," a source said.
Despite the fact that they are rumoured to now seeing new people, they are said to be committed to the kids.
"This is a natural evolution for Gwyneth and Chris as friends and as a couple. They remain close, and they remain totally committed to Apple and Moses. As they find their way forward as individuals, they will naturally be more public about seeing other people, if not showy about it," the source explained.