The 42-year-old actor, who recently sparked rumours of tying the knot with his girlfriend after being photographed wearing a silver band on his wedding ring finger, said they have not even discussed the idea yet, reported Contactmusic.
"I've never felt that pressure. No. It's not necessarily something I often think about. It's a whole other conversation. Don't forget how the institution of marriage came about," he said.
The couple also welcomed their first child, Ava Berlin, in March and Renner hopes to teach his daughter "compassion".