The Coldplay frontman has reportedly broached the idea of how Gwyneth Paltrow would feel about their children meeting his new friend.
Radar Online claims that Chris is so smitten with the young actress that he has told his estranged wife that he would like Apple, ten and Moses, eight, to meet her in the near future.
“Chris has fallen hard for Jen, and they are having a lot of fun together,” a source told the publication.
“It’s happened very fast, and it’s extremely intense. Apple and Moses haven’t met their dad’s girlfriend, yet. Chris hasn’t been discussing the relationship with Gwyneth, out of respect."
The source told the website: “It won’t be happening right away, Chris wants to make sure this relationship is going to just fizzle out before taking such a big step.
“He sees this relationship going the distance,” the source says.
Jennifer fuelled reports that she and Chris, 37, are very much an item when the actress was spotted attending two Coldplay concerts in the space of three days.
The 24-year-old star was most recently pictured walking around backstage at the 2014 iHeartRadio Music Festival in Las Vegas, where Chris and his band were performing.
While the pair have yet to confirm their romance or be pictured together at public events, the official Twitter account of iHeartRadio seemed to hint that the pair are going strong.
“SPOTTED #JenniferLawrence Backstage! Wonder who she’s here to see? *Cough New b/f #ChrisMartin Cough* http://ow.ly/BIaVz #iHeartRadio,” a post read.