According to the New York Post, Cole is in negotiations with producers about returning to the judging panel for the show's upcoming third season.
Cole, who was originally fired from the show after just weeks of filming, has previously appeared to scorn the possibility of returning and filed a $2.3m lawsuit against executives following her dismissal.
However, the reports allege that her return to the show could come as part of a settlement and suggest that the panel could comprise Simon Cowell and three women.
Previous rumours have suggested that Cowell would like Cole to return to the series, though it has also been suggested that she is wanted for the UK version of the competition. Cole's spokesperson later shot down the speculation.
The uncertainty about The X Factor USA's judging panel comes after LA Reid and Britney Spears confirmed that they will not be returning next season.
The future of the show's hosts Mario Lopez and Khloe Kardashian is also uncertain, though the New York Post claims that Kardashian will not be asked to return.
"They are asking Mario to come back, but not Khloe," a source explained.
Lopez has previously expressed an interest in returning to The X Factor, while Kardashian has explained that she believes she improved every week while hosting the series.
Elsewhere, Ne-Yo has revealed that he is in talks to appear on the judging panel, while mentor Demi Lovato has tipped Lady GaGa as a possible replacement for Spears.
However, a spokesperson for The X Factor has refused to comment on the reports, saying: "The producers have not yet made the talent decisions for this year."