Compton has 208 runs from his opening four Test matches against India at the start of the winter and Prior has said that he is backing the 29-year-old to score a century against New Zealand.
"He would want to have gone out and smashed a hundred [on his debut]," the Evening Standard quotes Prior as saying.
"He's hitting the ball brilliantly in the nets and it will be down to him to get his preparation right going into the Test.
"You can score all the runs you want in the world in warm-up games but ultimately that first innings of the Test match is where we want Compo to go and score a big hundred."
Compton has a 44.10 average in first-class cricket.