Can homosexual monks or nuns ordain, if not WHY? Namo Buddhaya! 
(I am a Theravada Buddhist)

The Vinaya says monks &amp; nuns cannot be together in private (it would be an offense). 


  But what if someone is a homosexual, how would they go about
  ordaining, as they would not be able to technically be with men then (similar to nuns)?


I would have a hard time believing the Buddha would discriminate against someone who is a homosexual. 

IF they cannot ordain, 


  what is the reason that they can't ordain as according to the Buddha? ( WITH SOURCE)


The Buddha chose to ordain woman, and homosexuals for sure can overcome their sexual urges just as a woman can towards men AS WELL, so why can't homosexuals ordain?

(Please, if possible, cite sources!)

Metta!
Homosexuals may fall under asittaka pandaka. They cannot ordain.


  asittakapandaka - A man who gains satisfaction from performing oral sex on another man and from ingesting his semen, and only becomes sexually aroused after ingesting another man's semen.


Source: Pandaka