The Sheffield band announced that they were returning to the studio earlier this month, just days after they met up at the Glastonbury festival, where frontman Alex Turner performed with The Last Shadow Puppets.
A source told The Sun: "The lads don't live in each other's pockets like they used to. Alex is always in London with his missus Alexa Chung while Jamie Cook is mostly in Sheffield.
"But when they got together at Glasto they realised they missed being together as a band. They had a good session and decided they wanted to start on the next album quickly. They've already got loads of songs and loads of ideas. Now it's just about getting it done."
The group's second album Favourite Worst Nightmare made a number one debut when it was released in April 2007.