The Girls Aloud star mentored Lloyd to fourth place on the 2010 series of The X Factor. However, since the competition ended, the 'Swagger Jagger' singer has previously said that Cole has not maintained contact.
Speaking to Real Radio North West's Real Breakfast Show earlier this week, Lloyd was asked if she would consider teaming up with the ex-judge, responding: "Maybe if she sings live with me."
When host Debbie Ousbey said that the remarks sounded like a challenge to Cole, Lloyd said: "Well it always is nowadays, when you haven't got the nifty little button to press."
Asked if she meant auto-tune, Lloyd laughed: "What, oh no? Never, never ever!"
Writing what seemed to be a response to Lloyd's dig, Cole last night tweeted: "Be Careful who you kick on your way up .. They kick you twice as hard on your way back down.. #unappreciationisugly (sic)."
Making no further comment, the 'Promise This' star - who is working on her third solo album in the US - added that she was "so excited to get home".
In the same interview, Lloyd also continued her ongoing spat with X Factor judge Louis Walsh, claiming that he should quit the show.
Cole has recently launched legal action against Now magazine, who published an interview with MC Harvey in which he spoke of an alleged relationship with her.
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Watch the video for Cher Lloyd's new single 'Want U Back' below: