The band said that Sheeran was an "inspiration" to them after he found success in the US earlier this year.
Andy Brown said: "We'd love to collaborate with Ed. He's an inspiration to us and we feel like we've both got into the industry through similar ways - gigging up and down the country for years before getting signed.
"He's also breaking the US which is again something we'd love to do. Hopefully for album two we'll get an opportunity to write a tune together."
The group's new single 'Standing in the Dark' is out this week and is currently in the top ten on the iTunes download chart.
Their debut album Chapman Square follows on October 22.
Watch Lawson perform an orchestral version of 'Standing in the Dark' with Vevo below: