The Daily Mail says the 16 year-old has agreed to move to City ahead of offers from Manchester United and Liverpool.
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The midfielder will move to City for an initial £600,000, which will rise to £2m should he reach the senior team.
Interestingly, Scotland youth international McMeekin also qualifies for England, with the FA keen to tempt him away.
He is yet to make his senior debut for Hearts, though has featured for the B team this season.