My urine test is positive for leukocytes and negative for nitrates, is that even possible for uti in my penis ?

Urethritis: A urine test with positive leukocytes suggests local inflammation, commonly in the bladder in women or the urethra ( tube carrying the urine from the bladder to the outside)in men. Inflammation of the urethra ( urethritis) is commonly caused by chlamydia infection, but may have non infectious causes also. Your doctor may prescribe antibiotic.