Reps for the actor did not respond to requests for comment.
The “X-Men” star and Costa met in New York last year, but are reportedly no longer dating.
This will be the third child for Marsden, 38, who is father to son Jack, 11, and daughter Mary, 6, with ex-wife Lisa Linde. The two were married for 11 years before filing for divorce last September.
Actor James Marsden is to be a dad again.
According to the NY Post, Marsden, who recently played Tina Fey's boyfriend on “30 Rock,” is expecting a baby with 24-year-old Brazilian model Rose Costa.