The youngster is one of several right-backs leaving Celtic this summer.
The newspaper claims Duffy is wanted by Celtic's league rivals, St Johnstone, after Aaron Comrie left for Dunfermline.
The 20-year-old is one of several youngsters set to leave Parkhead at the end of their contracts, along with PJ Crossan, Ross McLaughlin, Reece Willison and Regan Hendry, who has already agreed a two-year deal with Raith Rovers.
Duffy, a former Scotland Under-19 international, came through the ranks at Celtic but failed to make a senior competitive appearance.
And he is leaving despite the departures of Jeremy Toljan, Mikael Lusting and Cristian Gamboa in his position this summer.
Duffy will be expected to compete with the former Rangers right-back, Richard Foster, if he moves to St Johnstone.
Who should Celtic target to fill their right-back void?
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