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Anna Rothschild is not engaged to Tom D’Agostino Jr., and that 22-carat diamond ring she wears is a gift from another man, she told me.

The trans-Atlantic p.r. woman said from London that the rumors of an engagement to D’Agostino — who recently separated from “Real Housewife of NYC” Luann de Lesseps — are untrue.

“We’re best friends for 15 years. I adore Tom,” Rothschild said. “I would love to marry Tom because he’s such a great guy, but it’s bad timing for both of us.”

The $2 million ring she’s been wearing as she’s accompanied D’Agostino around town was a gift from another admirer. “I’m not saying who it was,” she said.

Sources say the gaudy gem came from Turkish art collector Ahmet Kocabiyik, who shared a Hamptons house with Rothschild two years ago. But Rothschild said, “I’m not making any comment about him.”

Rothschild, who has been divorced twice, also denied she had assumed the surname of the European banking dynasty. “It is my real name,” she said. “It’s the name I was born with.”