The Premier League giants recalled the youngster from his loan spell at Motherwell and have accepted an offer for him from the Championship outfit.
Grimshaw impressed during his loan spell at Motherwell and caught the eye of Preston manager Simon Grayson. The Championship club were keen to secure his services permanently and got in touch with Manchester United last week.
Grimshaw made 16 appearances for the Scottish Premiership side after joining them on loan last September.
Preston have enjoyed an amicable relationship with the Premier League giants having agreed two deals with Manchester United previously.