The 'Promise This' singer quit the ITV reality show last year in response to Cowell axing her from The X Factor USA mere days after she started.
The pair are believed to have made up since and the Syco boss claimed last month that Cole "misses" working on The X Factor.
However, her mentor will.i.am later stated that the 28-year-old would never return to the panel.
"Cheryl is part of The X Factor family," a source close to Cowell told The Mirror. "Formal discussions have yet to take place but if she wants to come back she would be welcomed with open arms."
An ITV insider added: "We'd welcome her with open arms. She was hugely popular and she's totally gorgeous. We'd love to have her back."
Cole is rumoured to be debuting the lead single from her upcoming third album on rival talent show The Voice UK, on which will.i.am is a coach.
The Black Eyed Peas star said at the weekend that he was hoping to "p*ss off" Cowell by securing her appearance on the BBC contest.