will.i.am assisted the X Factor USA star at the Judges' Houses stage of the competition and is said to have discussed the possibility of working with Cole during his visit.
"There were rumours earlier this summer that the pair were going to duet but it wasn't until this week that Britney and Will had the discussion," a source told the paper.
"He told Britney he was writing a great new track and wanted his 'two favourite girls' to record it together at his home studio."
will.i.am - whose album #willpower includes a track featuring Spears - is said to have told the singer that she would be "great" with Cole and apparently brought four tracks featuring the Girls Aloud star along to recording sessions.
"He's been trying to get them together since before he came on board as Cheryl's manager," the source added.
In the past, the Voice coach has also said that he would like Cole to work with Rihanna.
"I told Rihanna there was this girl called Cheryl Cole and she is the pop princess of England," he said. "I was telling people in America they should collaborate.
"Hopefully it will happen soon."