Sable, 43, currently assistant to Francesco Farioli at Ligue 1 leaders Nice, is the front-runner with former Hammarby boss Hellberg also heavily backed.
Owner Kyril Louis-Dreyfus is leading the hunt for a successor to Tony Mowbray, who was dismissed on Monday after a run of two wins in nine games left the Black Cats three points adrift of the play-off positions.
Louis-Dreyfus grew up in France and retains a five per cent share in Marseille, the Ligue 1 side who were owned by his family until 2016.
And it is there that he and director of football Kristjaan Speakman appear to be focussing their search, with 31-year old Reims boss Will Still also high on the club’s shortlist.
Sunderland considered making an approach for Farioli before he joined Nice from Antalyaspor in June but eventually opted to stick with Mowbray.
The 36-year-old is now unattainable, but Sable’s similar philosophy and background in youth coaching make him attractive to a club whose player-trading model is based on buying low and selling high.
However, there is not yet any indication that Sable desires the job and Nice would demand significant compensation.
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