Adding: "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."
Gwyneth, who celebrates her 42nd birthday this weekend, was reportedly shocked at the news.
The source revealed: "Gwyneth was absolutely stunned when Chris told her he wants to introduce the kids to Jennifer.
"It won't be happening right away, Chris wants to make sure this relationship isn't going to just fizzle out before taking such a big step."
"He sees this relationship going the distance," the source says. "This has been a huge blow to Gwyn's ego because she has always bragged that she has Chris wrapped around her finger."
Chris and Jennifer's relationship was revealed in August but they first sparked rumours of a romance after they were spotted in deep conversation at the after-party for Coldplay's Royal Albert Hall gig in London on July 1.
He is reportedly so smitten with the actress that he has been writing songs for her.
Jennifer Larence at the iHeartRadio concert with Chris Martin in the background. Photo / Getty Images
Over the weekend Hunger Games star Jennifer watched Chris perform at the iHeartRadio Music Festival in Las Vegas and the couple flew back to Los Angeles on a private jet together.
- Daily Mail