Ferguson is currently in charge of Everton on a temporary basis, following the dismissal of Rafael Benitez as manager earlier this month.
However, the Toffees are set to appoint ex-Chelsea boss Frank Lampard as their new permanent boss, despite Ferguson wanting the job.
Lampard will be assisted in the dugout by former Swansea and Derby County manager Paul Clement, which has put Ferguson’s future at the club under the scanner.
Ferguson was in the final shortlist of names considered by Toffees hierarchy for the manager’s role, but they opted to go with Lampard.
However, the Toffees caretaker boss could find himself taking over at another club soon, with Keys tweeting: “Big Dunc favourite for the Sunderland job I’m hearing. That would get everybody out of a hole.”
The Black Cats are set to immediately start proceeding to find a new manager, having shown Lee Johnson the exit door on Sunday, owing to a poor run of form and they rate Ferguson highly.
Sunderland have fallen to third in League One standings, out of the automatic promotion places, and it remains to be seen whether Ferguson will actually get the job to get their season back on track and possibly get them back into the Championship.
