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According to the Sun, Brendan Rodgers will return for the midfielder if James Maddison leaves the club. Rodgers tried to sign McGregor at the start of this season as well.
The Leicester City boss knows him well from their time together at Celtic and he could prove to be a quality addition for the Foxes.
McGregor is one of the best players in Scotland right now and he has the quality to make the step up to the Premier League.