The actor said that he wants to continue exploring his character Detective Stephen Holder and that reinventing the AMC series would be an "interesting" way to do that.
"We've invested a lot in these characters and want to see how they continue their journey," he told TVLine. "I feel like Linden (Mireille Enos) and Holder [are] just [getting] started.
"The series has to reboot itself... It's like the first season [of a show], where it [would] be original material and not based on the Danish [series] anymore."
Kinnaman added that he feels like he could only recently "spread... [his] wings" as an actor on The Killing.
"Season two was more fun for me to play because the framework [of season one] was that they wanted to put the audience in the place where they didn't know if they liked Holder," he explained. "They didn't know if he was a good guy or a bad guy.
"That's great from a series standpoint, but for me as an actor, wanting to play out all the colours of my character, that was a bit limiting."
Season two of The Killing concluded in the US on June 17. It currently airs in the UK Wednesdays on Channel 4.