The band's fourth album was released in March, and Fraiture said that they are already preparing new material for their fifth studio release.
Fraiture told Rolling Stone: "If we could do it tomorrow, that'd be great. But yeah, as soon as possible I think."
He added that the New York band plan on recording the new album in the same way as Angles, with each member of the band putting their ideas forward.
"It's been feeling really good. We're kind of doing the same thing as the last record - we're bringing in parts and ideas and kind of just working on those and trying to make sense of them, coming from five different people."
Fraiture had previously hinted that the band were already working on new material a month after Angles was released.
The Strokes will perform at the Reading and Leeds Festival, including a headline slot in Reading on August 27.
Watch the video for The Strokes' 'Under Cover of Darkness' below: