Costner, 68, and the 49-year-old singer were in the British Virgin Islands last month as part of a tennis fundraiser for Jewel’s Inspiring Children Foundation.
In photos obtained by TMZ, the Yellowstone alum could be seen wrapping his arms around the singer while she spoke into a microphone.
A source told the tabloid that their relationship is “rather new.”
“There was definitely something going on. They were flirty. And when they were together, it was like they both just lit up,” the insider dished.
“You could tell they were trying to be discreet, but anybody who saw them could tell something was going on,” another source claimed.
The alleged lovebirds reportedly left the Caribbean together.
The “Foolish Games” singer documented the trip on her Instagram account last month, noting that Costner was “kind enough” to act as a mentor.
“Every year, my foundation @inspiringchildren and I go to Necker Island to help host a tennis event [with] @richardbranson to raise funds for our kids. Amazing players like @geniebouchard come and support us in playing doubles with the folks who come… it’s an incredible time, and one I use to relax, rest and play w[with] my son!” she wrote.
Jewel was previously married to professional cowboy Ty Murray.
They share one child together, son Kase, 12.
Costner was married to Christine Baumgartner for 18 years. The designer filed for divorce in May.
The exes, who share Cayden, 16, Hayes, 14, and Grace, 13, settled their divorce in September.
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Gallery Credit: Ryan Reichard