The Scottish attacking midfielder scored seven goals and provided three assists in 23 games for the Under-18s last season after joining the Toffees in July last year.
However, journalist Fabrizio Romano claims that Lawrence will be leaving Everton this summer and he is soon set to announce which club he will be joining.
Romano adds that the teenager has attracted interest from the "big six" Premier League clubs, but Man City are currently the favourites for his signature.
Lawrence, who also made three appearances for Everton's Under-21s last season, is yet to sign on for the club as a scholar, meaning the Toffees can receive a compensation fee from interested clubs.
The teenage starlet could be joining a Man City academy which has produced a number of talented players in recent years including the likes of Phil Foden, Jadon Sancho, Cole Palmer and James McAtee.