The pair are said to reportedly be spending Thanksgiving weekend together, reported People.
"He thinks she's a cool girl. She's always been into him, but he's starting to like her more and more," a source said.
Rumors that something was happening between Jonas, 27, and Turner, 20, started doing the rounds last weekend after the duo was spotted getting cozy at a pre-MTV Europe Music Awards event.
"They seemed pretty comfortable. They were really close together," the source said.
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