Baldwin, 55, recently wrapped his seven-season, award-winning stint on the network's sitcom "30 Rock." He can currently be seen in the Broadway play "Orphans."
The Times said Baldwin is being courted as NBC reworks its entire late-night television lineup. The network announced last week Jimmy Fallon is to replace Jay Leno as host of "The Tonight Show," starting next year. However, Fallon's successor on "Late Night" has not yet been named.
The Times said Baldwin, who has interviewed celebrities for a successful series of WNYC radio podcasts, might get a similar late-night program in the half-hour 1:35 a.m. time slot now occupied by Carson Daly's "Last Call."
Daly is also the host of NBC's prime-time singing competition series "The Voice."
Notable deaths of 2014 [PHOTOS]