Martin, who separated from wife Gwyneth Paltrow in March after 12 years of marriage, is dating Lawrence since late June, after she split from her actor Nicholas Hoult, reported Us magazine.
Lawrence was recently spotted at the singer's concert in New York City, where multiple eyewitnesses say she got a special shout-out from the stage.
Onlookers said Martin appeared to blow a kiss in the Oscar winner's direction. She and some friends were seated in an upstairs VIP booth overlooking the stage.
Both the stars were also in attendance at a bash in London in early July, an after-party for Coldplay's show there, according to another insider.
No representatives for Lawrence, 24 or Martin, 37, have commented yet on the reports.