The former X Factor judge is currently working on her third solo album, and is said to have been teamed up with the 'Love The Way You Lie' producer by her manager will.i.am.
"Cheryl and Alex have struck up a great relationship and have been living in each other's pockets for the past week," a source told The Sun. "Some of the recording sessions have run into the very early hours with just the two of them and a laptop in their hotel rooms.
"Cheryl has been suffering from jet lag and couldn't sleep, so they have just worked through the night. It hasn't all been work - they've enjoyed some play too. If the music is going to work then they need to find their own chemistry."
Alex Da Kid - whose real name is Alexander Grant - previously played football for Bristol City. However, he gave up football at the age of 19, studying music technology at university and forging a successful producing career.
Cole has told fans on Twitter that she is "frustrated with excitement" about sharing her new material.
> Cheryl Cole working with Taio Cruz on new album
Watch Cheryl Cole's 'Promise This' video below: