|Baldwin and Thomas on their wedding day|
The '30 Rock' star and the 'Extra' TV correspondent - who have been married for seven months - are said to be "so excited" about their news but the couple have only told "really close friends and family" about her pregnancy.
Hilaria's friend told In Touch Weekly magazine: "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.
"[Hilaria] has not said much to anyone as far as how far along she is. She is so healthy and a yoga freak, so everyone could tell right away something was different. Hilaria has told only really close friends and family she is pregnant, only a close circle she trusts."
Alec's PR company Hiltzik Strategies has refused to either confirm or deny the news of Hilaria's reported pregnancy.
The firm wrote on Twitter: "Part 1 -re: @abfalecbaldwin / @hilariabaldwin: Our response to baby speculation over the past 18 months has remained the same...
"pt2: re:@abfalecbaldwin/@hilariabaldwin. ..when/if Alec&Hilaria have news they want 2 share, they will share it. Until then, no comment. (sic)"
Hilaria sparked speculation she was expecting on Monday when she showed off what looked like a baby bump while filming a segment for 'Extra' that saw her pull off some impromptu dance moves.
The 54-year-old actor - who already has a 17-year-old daughter, Ireland, with ex-wife Kim Basinger - has recently said he would love the couple's future children to look like Hilaria.
He said: "My only dream is they look like her."