The boy band's Carlos Pena Jr. told BANG Showbiz: "One of our first shows was with Justin Bieber, and at that point he was very shy.
"It's nuts to think about how he's blown up, but we'd love to write a song with him, he's very talented, that guy works his butt off, he puts in the work."
"get off our patch" by a text message when they appeared on TV show 'Daybreak', however Big Time Rush aren't worried and would like to play on the same bill as their rivals.
Logan said: "And JLS we looked up and we heard a bunch of their songs and their harmonies are killer and to me that makes me want to strive and get to that level. Pop music makes the world go round, so the more the merrier. We'd love to do a tour with them or something, that would be really cool."
Big Time Rush play London's The O2 shepherd's Bush Empire tonight and 'Boyfriend', featuring Snoop Dogg is out now.