So is a reconciliation in the works for the couple?
"They haven't made any concrete decision to get back together yet, but clearly it's a possibility," a friend of the couple tells PEOPLE. "At this point, some of the pressure was just taken off them – pressure they put on themselves to 'make it work.' "
Though Martin, 37, spent a few weeks living in Malibu after the split, he's since moved back to the Brentwood home he shared with Paltrow, 41, and their two kids, Apple, 10, and Moses, 8, when he's not touring with Coldplay.
"They have spent more time together than they did when they were a couple," says another source. "When they are out together, all they do is laugh and act flirty and playful."
And though it's yet to be seen if the duo – who were married for 10 years – officially recouple, friends say the two will always have something in common: their dedication to their kids.
"Gwyneth didn't want to end the marriage and is happy that she and Chris still have a close relationship," says an insider close to the family. "He's been a great father and that has helped keep the flame alive."
Adds the friend: "They clearly love each other and always will, and if the romance comes back, they'll go with it if it feels right."
Reporting by JENNIFER GARCIA and LINDA MARX