The former Will and Grace actress suggested that Streisand could join the NBC musical as the mother of her character Julia.
Asked by The Huffington Post what celebrity cameo she'd most like to see, Messing replied: "I think it would have to be Barbra Streisand. Funny Girl was my favourite movie growing up, and she was my idol.
"She started out on Broadway, and I think it would be great if she would come on and play my mother."
Messing also revealed that she is facing the "terrifying" prospect of more singing in Smash's second season.
"I was told that Julia would be singing this season, which is a little terrifying, but also a little exciting," she said. "But the music is one of the things that makes Smash so special.
"As Julia, I get to sit on the other side of the table and listen to the music being sung. So I get to go to work and get front row centre seats. I love it."
It was recently confirmed that Messing will reunite with Will and Grace co-star Sean Hayes on Smash.
Rescue Me star Daniel Sunjata has also been cast as Julia's new love interest.