The British rock band from Sheffield released successful album AM in 2013, and Alex admitted the group hasn't even started work on follow up material.
Instead, the rocker has been busy playing shows with his other band, The Last Shadow Puppets, alongside Miles Kane, James Ford and Zach Dawes.
When Alex stopped by Britain's Radio X for a chat, he admitted Arctic Monkeys fans shouldn't get their hopes up about another album being imminent.
“No, there aren’t really, not yet," he said as to whether any new music was pending. "But there will be at some point. I mean, we’ll see with that. No rush," he shared.
“The plan was to end (The Last Shadow Puppets) at the end of the summer, and I think we’ll stick to that," explained Alex.
The Last Shadow Puppets are playing two dates at London's Alexandra Palace on 15 and 16 July (16), followed by performances in countries including France and Denmark.
The group most recently wowed with a set at Glastonbury (24-26Jun16), where the musicians played a cover of the late David Bowie's Moonage Daydream to an excited crowd.
Arctic Monkeys drummer Matt Helders has been kept busy too, playing as part of Iggy Pop's band on his Post Pop Depression Tour alongside Queens Of The Stone Age's Josh Homme,