Ledley moved to Derby on a short-term deal in September and is yet to taste defeat in eight appearances so far, with the Rams' only loss in that time coming in the Welshman's absence.
Ledley's contract expires on New Year's eve and the report claims that Derby want him to sign a new one.
18 points and 17 places separate Derby and bottom-club Sunderland, and the 30-year-old may have reservations over sacrificing a potential promotion push to fight against relegation.
Nevertheless, the opportunity to reunite with Chris Coleman - his Wales manager for five years until last weekend - will likely appeal to Ledley.
Sunderland have recently lost Ledley's fellow Wales midfielder, Jonny Williams, for up to three months.
Ledley began his career at Cardiff City and later turned out for Celtic and Crystal Palace, who released him earlier this year.
Could Ledley swap Derby for Sunderland?
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