The 'Hunger Games' star - who is reportedly romancing the Coldplay frontman - is said to have got the seal of approval from his children, Apple, 11 and Moses, nine.
A source told US' OK! magazine: "Jen's completely won Apple and Moses over. Chris has been joking that they only come over to see Jen ...
"Apple's completely in awe of Jen, who's been incredible with them both. They adore her."
Meanwhile, a source recently claimed the couple are keen to keep their relationship as private as possible unlike Chris' relationship with his soon-to-be ex-wife Gwyneth Paltrow.
The insider shared: "Jennifer's really into Chris - she just wants to keep their relationship under wraps because she saw what happened with Gwyneth and she doesn't want that kind of press."
Another source also insisted the pair are "happier than ever", after rumours they had parted ways.
They added: "Both have full plates and they like it that way. They see each other when they can, yet each continues to do their own thing. They respect each other immeasurably.
"[They] are happier than ever. They have been spending a lot of time together."