According to Radar Online, the 37-year-old singer is ready to introduce Jennifer to his children with ex Gwyneth Paltrow, Apple, 10 and Moses, eight, after just two months of dating.
"Chris has fallen hard for Jen, and they are having a lot of fun together," a source told Radar. "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 also made it clear that this hasn't gone down well with Gwyneth.
"Gwyneth was absolutely stunned when Chris told her he wants to introduce the kids to Jennifer," the source said. "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."
Neither Lawrence or Martin have confirmed they are together, but rumours first started when Jennifer was seen backstage at a Coldplay gig in London in August.
Since then, Lawrence joined Martin at the HeartRadio Music Festival in Vegas where she supported the Coldplay frontman after his set.
The people at iHeartRadio weren't shy of fuelling rumours further either. The brand tweeted on the night: "SPOTTED #JenniferLawrence Backstage! Wonder who she's here to see? *Cough New b/f #ChrisMartin Cough*"
It sounds like this celebrity romance could be blossoming.
Love J-Law? So do we...