The group said that they have pitched a track to Cole's team and hope that it will appear on her forthcoming record.
In an interview at a London recording studio, Ben Adams told Mark Boardman: "We are in a writing session today, so a publisher will give us a briefing for a type of song they are looking for. Right now we are working on one we are hoping to pitch for Cheryl Cole.
"It's very different. Sometimes we get sent requests, [but] it's always better to get the artist in the studio and write what they want and write with them."
Mark Read added: "We are just pitching the track [for Cole], we are writing for her. Her team are looking for songs to put on her next album.
"While we've been here, I've written for many great artists, [including] John Barrowman's last single 'I Owe It All To You', which also happened to be the only new track on his album."
A1, who scored eight Top 10 hits in the UK between 1999 and 2002, recently played a one-off gig at London's Islington Academy in support of their latest album Waiting For Daylight.
Cole recently told fans that she had wrapped up work on her third record, tweeting: "Yesss! The album is DONE !!! *dancing all over the place* I'm Soooo HAPPY and EXCITED to share with you !! #CherylMusic on its way.. Booyaa. (sic)"
Watch A1's 'Same Old Brand New You' music video below: