Chris Martin and Gwyneth Paltrow
Chris Martin and Gwyneth Paltrow enjoy a spa day out with their childrenGetty

Consciously uncoupled Gwyneth Paltrow and Chris Martin could be getting back together after the Coldplay singer ended his relationship with Jennifer Lawrence.

The former couple who announced their separation in March this year, were spotted with their children Apple aged 10 and eight-year-old Moses in Tribeca's i-Plaza Nail & Spa.

"They seemed very affectionate toward each other," a source told PageSix.

The estranged couple "were laughing a lot, making jokes, and Chris even had his arm around Gwyneth," said another source.

Martin also entertained his children by dancing and singing along to Christmas carols playing in the salon, while he waited for Apple to finish her manicure.

Earlier in March, 42-year-old Paltrow famously called their split "conscious uncoupling", announcing that she and Martin are separating after 10 years of marriage.

After their split, the actress has been linked to Brad Fulchuk, while Martin dated Jennifer Lawrence, but currently both are single.

Previously, the couple were reportedly spotted in Texas, where they seemed "inseparable" during the opening of a Goop store in Dallas.

A source told Hollywood Take: "They tried to avoid the cameras, but he stuck to her like glue. There was a tenderness that you'd associate with a couple in love."

Paltrow and Martin also travelled to New York to support Cameron Diaz when she hosted Saturday Night Live.

"Despite being separated, they've been awfully affectionate! There's buzz among their friends that they are still sleeping together," a source said.

"They even stayed in the same hotel rooms in both Texas and New York."