Former Bhoys boss Brendan Rodgers knows all about McGregor.
Football Insider claims the 27-year-old could join Rodgers in the Premier League.
Leicester wanted him last summer as well.
And with Celtic out of the Champions League this week, the money Leicester can offer may be too good for the Scottish champions to turn down.
But it is unclear if McGregor wants to make the move, as he may want to try and win a historic 10th Scottish title in a row with Celtic instead.