The group are currently working on their fourth studio album and want the Canadian rapper to feature on the lead single for the collection.
"We'd love to do a record with Drake and we're going to approach him to feature on our next single as it has to be our best yet," Marvin Humes told the Daily Star.
"I really want to see both him and Rihanna at Wireless Festival."
Speaking about what they want to achieve with their next album, Humes explained: "Options are not good enough - we need an out-and-out smash. We're going to Scandinavia and America over the next few weeks to put pen to paper.
"Our fourth album is pivotal to our career. While we're very proud of what we've achieved – we've sold five million albums so far – the next album has to take us international."
Band member Oritsé Williams recently revealed that JLS have decided to work with top US producers for the follow-up to Jukebox as they want to record "a great album".
> JLS's Oritsé Williams: 'I've written a song for Usher'
Watch the music video for JLS's 'She Makes Me Wanna' below: