Multiple sources tell E! News the 24-year-old actress and 37-year-old Coldplay frontman have "been spending quality time together" since Lawrence split from boyfriend Nicholas Hoult in late June.
Lawrence and Hoult started dating in 2011, and broke up in January 2013. The couple rekindled their relationship in July 2013, and news of their new breakup broke August 1. The split is said to have been friendly, and came about because of their busy careers.
Martin married Gwyneth Paltrow in December 2003, and the pair "consciously uncoupled" in March. They are currently separated, and have two children together, 10-year-old daughter Apple and 8-year-old son Moses. Martin and Paltrow were still living together as of June.
Lawrence will appear in Serena and The Hunger Games: Mockingjay - Part 1 later this year. Martin and Coldplay released their sixth studio album, Ghost Stories, in May.