The Knicks have convinced at least one faction they are extremely serious about trading for or buying a late first-round pick with the NBA Draft less than a week away.

When shooting guard P.J. Hairston agreed to work out for Knicks president Phil Jackson on June 5, it was the strongest indication they are setting their sights on more than just buying a second-rounder next Thursday night.

Hairston, the controversial former North Carolina standout who was expelled from school last December, is slated to go between the 20th and 30th picks. He has worked out for about a dozen teams, mostly clubs in the lottery.

“The interest level is very, very high,’’ Hairston’s agent, Juan Morrow, told The Post. “You never know what Phil Jackson has up his sleeve.’’

Morrow admitted even if the Knicks can’t make a deal — and there are enough teams with multiple first-round picks looking to trade, such as the Thunder and Suns — it was an honor for Hairston. Jackson took control of much of the workout which came before new coach Derek Fisher was hired.

“Any kid growing up watching Phil Jackson’s teams, when he wants you to work out for him, you do it,’’ Morrow said.

Jackson loves big guards and Hairston fills the bill at a solid 6-foot-5, 240 pounds. It may be worth giving up on combo guard Iman Shumpert, whose rookie contract expires after this season and who could be due a bigger payday.

After his North Carolina fiasco, in which he was caught driving cars that apparently had been rented for him, Hairston latched on in the D-League for the Texas Defenders in January and drove up his stock.