Billy Joel has given his hot young squeeze an “engagement ring” – but not a marriage proposal, The National ENQUIRER has learned. 

The thrice-divorced “Piano Man,” 65, presented the pricey sparkler to Alexis Roderick, 32, two years ago, but she’s still waiting for him to make it official, sources said.

“It wasn’t really an engagement ring,” explained the source, “but it was more than a friendship ring.

“Billy hasn’t ruled out getting married again, but as far as I know, they’re happy and not in any rush.”

Billy’s rep told The ENQUIRER there was “no comment” on his “engagement” to Alexis, a former financial advisor for the investment bank Morgan Stanley.

But a close friend of Alexis told The 
ENQUIRER: “She gave up a promising career in finance to be at Billy’s beck and call. She’s been with him for five years and deserves to make it official.”

Still, Billy, who’s worth an estimated $180 million, may be wary of dipping his toes back in the marriage pool as a result of his failed marriages, including one to “Uptown Girl” Christie Brinkley.

“Some friends are even telling Alexis she ought to give Billy a ‘marry me or set me free’ ultimatum,” her pal added.