The 48-year-old emerged as a shock contender to take over from Brendan Rodgers, who tendered his resignation in October.
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According to the Daily Mail, MLS side Columbus Crew have now granted Nancy permission to speak to Celtic powerbroker Dermot Desmond.
The report adds that there is a growing expectation the Frenchman will be in the dugout by the time Celtic take on St Mirren next Saturday (November 22).
Nancy, who was largely a lower league player in France before moving to Quebec in 2005 to play for a university side, has never managed in Europe.