The 48-year-old has been touted to replace Brendan Rodgers, who left the club over a fortnight ago.
One bookmaker has suspended betting on the next permanent Celtic manager due to Nancy's odds being so short.
He once received high praise from Arsenal legend Thierry Henry, who referred to him as the first black manager to win the MLS Cup.
Henry said on live television: "From the bottom of my heart, I know how important it was for you, to be the first one and to do it your way.
"I know how hard you work, I know how much a lover of the game you are, and how you like to see the game being played a certain way, to be on the ball, to possess the ball.
"From the bottom of my heart, well done."
Nancy served as Henry's assistant manager at CF Montreal before taking over as head coach.
He led the Crew to MLS Cup victory in 2023, a feat that earned him Henry's admiration.
Martin O'Neill remains in interim charge of Celtic.
The club's management is reportedly in talks with potential candidates for the vacancy, with Nancy believed to be among them.