The 54-year-old was previously married to Kim Basinger but divorced her in 2002.
The actor got engaged to Thomas in 2011, reported a website. "The engaged couple have been telling people they'll be spending time in Europe. There's speculation they're going to get married.
He has set time for possible nuptials post-Cannes work plans in Europe," a source said. Baldwin met Thomas in early 2011 while dining with friends at a posh restaurant.
The 'It's Complicated' actor was said to have proposed to the 28-year-old during a trip to the East End of Long Island.
His representative confirmed the engagement in April by tweeting, "Alec proposed to Hilaria this weekend and we're all excited for the newly engaged couple."
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