Avril Lavigne and Tyga Are 'Very Into Each Other' and 'Spending a Lot of Time Together': Source

Avril Lavigne and Tyga are enjoying each other's company.

"They're very into each other," a source tells PEOPLE about the "Girlfriend" singer, 38, and "Rack City" rapper, 33, who have been romantically linked since they were spotted having dinner at Nobu in Los Angeles last month. They were later seen sharing a kiss during Paris Fashion Week.

They don't plan on rushing into a relationship, however, says the insider.

"They're still not exclusive and just getting to know each other. They're taking things very slowly to be on the safe side and really get to know each other before diving into something serious," the source adds.

"But they are spending a lot of time together," they add, noting that Tyga will be focused on his career soon. "He's about to get locked in working on new music."

Despite taking things slow, Tyga has gone all out and bought an $80,000 necklace for Lavigne.

The custom-made jewelry from Mavani & Co Jewelry features 50 carats of white and black diamonds, as well as pink sapphires, founder Eric Mavani confirmed on March 19.

In an image of the necklace shared on Instagram, the piece can be seen with several pendants on it, including two of the letter "A" written over a pink heart, as well as two skulls and crossbones accessorized with pink ribbons. Lavigne's first name also takes center stage at the front of the necklace.

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Lavigne's quality time with Tyga comes after her breakup from Mod Sun.

"Avril and Mod Sun have been on and off for the past two months, but are no longer together as a couple," an insider told PEOPLE in February.

Amid news of her romance with Tyga, Lavigne's ex-fiancé shared a reflective message on Twitter about the people in his life.

"I'm so grateful to have real friends who will sit on the phone with me for 2 hours. If you got those people in your life, do not let them go," he wrote the same day Tyga and Lavigne were seen kissing.

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A week before that, the musician shared similar thoughts when speaking out about the split for the first time — which happened less than a year after he and Lavigne got engaged.

"In 1 week, my entire life completely changed… I just know there's a plan for it all. I'll keep my head up + always listen to my heart, even when it feels broken," he shared in an Instagram post alongside a photo of himself. "Being surrounded by love every night on tour has been an absolute blessing. I have the best friends in the entire world, thanks for always having my back. See you on stage."