Boro will entertain the Minstermen at the Flamingo Land Stadium, with the date of the game yet to be confirmed.
Kittrick said: "I go to the gym in my Scarborough Athletic shorts and there is a York fan that goes there regularly, so I'm already aware of the banter that will go on in the build-up to the game.
"It is one that the fans will be looking at, thinking will we, won't we, can we, can't we.
"It is also one that the players will be looking at because it is an exciting tie.
"This will be a good test for our lads and also a test for York City.
"I'm not sure how they will treat it, but this is a game that we will look at like every other one - we want to win it.
"Momentum is the key and a win in that match would be massive for us."