"Our response to baby speculation over the past 18 months has remained the same," tweeted Baldwin's representative, Matthew Hiltzik. "When/if Alec&Hilaria have news they want 2 share, they will share it. Until then, no comment."
However, Thomas sent out this cryptic, but intriguing tweet Wednesday: "When love and skill work together, expect a masterpiece -- John Ruskin," citing the 19th-century English art critic.
Baldwin, 54, has a 17-year-old daughter, Ireland, with his ex-wife, actress Kim Basinger.
The two-time Emmy Award-winner, who married Thomas, 28, last June, told CNN's Piers Morgan in an interview a year ago that he would like to have more children. "Oh, sure, that would be great," he said in response to Morgan asking, "Have you thought about any little Alec Baldwins?"
"That would be heaven," he continued. "That would be fantastic."