A source tells PEOPLE that the couple appears to be taking their relationship to the next level as they get to know each other away from the spotlight
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It’s just low-key love for Dakota Johnson and Chris Martin.

A source tells PEOPLE that the couple appears to be taking their relationship to the next level as they get to know each other away from the spotlight.

“For the past two weeks, they have spent a lot of time together,” says the insider. “Chris lives in Malibu and Dakota seems to love hanging out there. They occasionally go for dinner with friends, but mostly have friends over at home. They go to the beach together, and walks around the neighborhood. They seem to enjoy sharing a quiet life. It does seem they are getting more serious.”

Some of their recent outings have included a group trip with friends to the Little Beach House in Malibu on Friday and lunch last week at Gjelina in Venice.

“They snuggled up to each other during lunch. They looked very happy,” says a source. “They arrived and left together.”

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Dakota Johnson and Chris Martin
| Credit: Venturelli/WireImage; David Becker/Getty Images for iHeartMedia

The Fifty Shades actress, 28, and the Coldplay frontman, 41, showed some rare PDA while walking her dog Zeppelin in Malibu on Sunday. Johnson reached behind Martin and sweetly grabbed his hand while they strolled.

The actress and the musician first sparked gossip after being spotted on a mid-October sushi date in Los Angeles. They were “cozy, laughing and affectionate,” said a source at the time, adding that it was just the two of them at dinner.

About a month after they were first seen together, Johnson was photographed hanging out in the sound booth at Coldplay’s concert in Argentina. Fans in the crowd spotted the actress and excitedly posted pictures on social media as she hung out during the show.

Since then, the two have been spotted on dates around Malibu and Los Angeles and even arrived hand-in-hand to Ellen DeGeneres’ 60th birthday party in February. The two were seen holding hands as they caught up with Drew Barrymore outside the bash, which Martin’s ex-wife Gwyneth Paltrow also attended with boyfriend Brad Falchuk shortly after announcing their engagement.

RELATED VIDEO: Dakota Johnson, Chris Martin Hold Hands at Party Attended by Gwyneth Paltrow and Brad Falchuk

Johnson has a history with musicians, having previously dated model/rocker Matthew Hitt. The two have been on and off for years, but were last seen together in 2016. Martin was last linked to British actress Annabelle Wallis. The two began dating in August 2015, and were often spotted together as the singer toured with his band.

The singer was also married for 10 years to Paltrow before the pair split in March of 2014. The two have remained close, often spending time with their children, Apple, 14, and Moses, 12, together.