If the reports are confirmed, this would be the first child for the couple, who married in June 2012.
© Rex Features / Startraks Photo/Rex Features
InTouch Weekly has claimed that the 30 Rock star and his wife - a yoga instructor - are expecting.
"Hilaria has told only really close friends and family she is pregnant, only a close circle she trusts," an insider is quoted as saying. "They are both so excited, and Alec is so in love with her.
"She says she is so in love with Alec, and he tells all her friends that she is the best thing that has ever happened to him."
© WENN / Apega/WENN.com
© WENN / Apega/WENN.com
[Left: Alec Baldwin with wife Hilaria Thomas/ Right: The actor with his daughter Ireland]
Meanwhile, a spokesperson for the Baldwins declined to confirm or deny the magazine's claims.
"Our response to baby speculation over the past 18 months has remained the same," said publicist Matthew Hiltzik on his company's Twitter account.
"When/if @abfalecbaldwin and @Hilariabaldwin have news they want to share, they will share it. Until then, we have no comment."
The Departed actor Alec is already father to 17-year-old daughter Ireland from his marriage to LA Confidential star Kim Basinger.
View all of today's best celebrity pictures - Photo gallery:
Tom Sturridge and Sienna Miller hold hands in the back of a cab after dining at Lulu's restaurant in Mayfair, London.
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