Masturbation is one method that some unmarried men have chosen rather than participate in sex outside of marriage. Jesus spoke to this issue directly, "But I tell you that anyone who looks at a woman lustfully has already committed adultery with her in his heart." Mt 5:28 Christian men knowing that Jesus said this want to be able to masturbate while not committing lust.
I have men tell me that they just imagine female body parts or women that they make up in their own minds cause sexual arousal.
Is imagining female body parts or women you make up acceptable?
Maybe. The intent of the young man is trying to please God with his expression of his sexuality in a "safe" way, honoring what Jesus said. His heart is seemingly in the right place.
Is imagining female body parts or women you make up acceptable?
No. What is something that may make it unacceptable? The sexual response, even the human sexual response is subject to behavioral conditioning. The Encyclopaedia of Sexual Behavior, by Albert Ellis lists sexual stimulation in over 70 different ways. It seems that many of them (i.e. arousal by touching feet) have come about from a learned response, pairing a stimulus with a reward. For example, go to this blog post about a young man who inadvertently trained his sexual response (http://www.ironstrikes.com/blog/training-your-sexual-response1).
So, if the human sexual response can become conditioned, then conditioning one's response to imagined female body parts, could result in a fetish. Conditioning one's response to a make believe woman can result in comparing one's future wife to this made up person. This could make it difficult to find a spouse that could live up to these conditioned expectations. Also, as we discussed yesterday, imagining such could also be an entry into the world of the supernatural (http://www.ironstrikes.com/blog/demonic-masturbation)
What we do know is that God has designed the male body for expression of sexuality in a safe manner for an unmarried guy. God has built in a way "to pop the cork" when hormones become strong. He has built in wet dreams. The male body takes care of itself. To purposely dream (lucid dreaming) of a sexual encounter reaches into the realm of the unacceptable (http://www.ironstrikes.com/blog/sexual-dreaming) but many of our dreams are not under our conscious control.
So, now you have a clear answer: maybe, no, God's way.