Calvin Klein’s younger boyfriend, Nick Gruber, is headed to rehab after being arrested for possessing cocaine and getting in a brawl with a pal, sources confirmed to Page Six. A spy tells us Gruber was seen leaving his luxury 666 Greenwich St. building “with a wheelie suitcase” and talking about his impending trip to rehab yesterday. A source said, “He was talking about how there would probably be photographers outside, and also when he got to rehab.” The spy added, “He was talking very fast, and he kept sniffing. But when he walked out of the building, there were no photographers there.” The 22-year-old ex-porn star paramour of 69-year-old fashion icon Klein allegedly clocked Calvin Swint, 20, an intern for New Jersey Sen. Frank Lautenberg, on the balcony of Gruber’s swank penthouse (the rent is paid by Klein, sources tell us) during a 4:20 a.m. fight this week. Sources told The Post that when cops arrived, Gruber tried to avoid being cuffed and shoved his hands into his pants, where cops allege they later found cocaine. He was arraigned on a felony charge of possessing a stimulant and two misdemeanors — resisting arrest and assault with intent to cause physical injury. He has retained powerhouse defense lawyer Ben Brafman, who did not comment last night. Klein, who was treated for alcohol and prescription drug abuse at Minnesota’s Hazelden Institute in 1988, has spoken openly about his battle to stay sober, and announced in 2003 — after an outburst at a Knicks game — that he was again seeking treatment for a drug problem.