United will play Blackburn at Elland Road on Saturday, travel to Newcastle on Wednesday, July 29 and take on Burnley at Turf Moor on Saturday, August 1, with games against Bradford Park Avenue and Forest Green Rovers in between.
Grayson said: "We've used the games so far to build up to three big games now against Blackburn, Newcastle and Burnley.
"These are great games and the teams we are playing have some great individual players. If we want to get back to the level we want we have to perform against these teams."
Leeds have drawn three, won one and lost one of their five friendly matches so far.