The former Chelsea defender joined Sunderland last summer and made only 18 Premier League appearances for the Black Cats.
The 28-year-old does not have a long-term future at Sunderland and his performance this season so far has been largely unconvincing.
According to reports from Sunderland Echo, Djilobodji is in talks with Ligue 1 side Dijon over a potential season-long loan move.
Sunderland spent £8 million for his signature, but failed to live up to expectations at Wearside.
His departure will at least free up the wages, which will help Grayson to bring in one or two new players on deadline day.
The Magpies have been linked with a move for Argentine left-back, Nicolas Tagliafico, but it seems they’ve shifted their focus elsewhere.
Rafael Benitez is keen to add another full-back before the window closes after an injury to Paul Dummett.
The 21-year-old signed a new five-year deal at St Mary’s this summer, and would be only available on a loan move.
The report adds that Newcastle are now in pole position to sign him on loan on the deadline day.