The Avengers star, 42, allegedly dated the unnamed mum-to-be last year (12), and although they are no longer together, he has allowed his former lover to stay in his Los Angeles home.
A source tells Us Weekly magazine, ""They used to date but it wasn't serious. He's being ultra-secretive about it, but she has been going on about her life and not hiding it (her pregnancy).""
Sources tell the publication Renner was overheard telling TV beauty Eva Longoria about the baby news at the Golden Globe Awards in Hollywood on Sunday (13Jan13). The baby is reportedly due next month (Feb13).
Renner previously dated aspiring actress Jess Macallan, but the couple split in 2010 after four years together.
The actor's publicist had yet to respond to requests for a comment as WENN went to press.