Johnstone enjoyed a successful spell on loan at Preston in the second half of last season, playing a key role in helping the club secure promotion to the Championship.
The 22-year-old impressed Simon Grayson during his loan stint at Deepdale and the Preston boss was keen to sign the shot-stopper on a permanent basis.
However, United have rebuffed Preston's bid with the England Under-20 international featuring heavily in the Red Devils' pre-season tour of America.
Johnstone has appeared in all of United’s games on their pre-season tour and the academy product has caught the eye this summer.
With Victor Valdes on his way out of Old Trafford following his bust-up with Louis van Gaal and the ongoing saga regarding David De Gea's future still unresolved, United are keen to keep hold of Johnstone.
Preston remain keen on Johnstone despite the signing of Jordan Pickford from Sunderland on loan, and once United resolve their goalkeeping situation the Championship new boys are expected to make a new move for Johnstone.