Answer:
If you truly are not having an intimate relationship then there is not sin in the relationship.
However, there are two things to consider, the first is from the Bible and the second is an old Chinese proverb.
There are many verses in the Bible about being a good witness and not being a stumbling block to someone else coming to the gospel, such as:
1 John 2:10 He that loveth his brother abideth in the light, and there is none occasion of stumbling in him.
Would other people really believe the two of you live together without some sort of relationship and would you doing so cause someone else to stumble. Also, it would be very hard for you to tell someone else not do live together when you are even though they may in fact be doing much more. Paul talks about this and says he would rather not do things that even if for him they were not wrong but for someone else it would be 1 Corinthians 8:13 Wherefore, if meat make my brother to offend, I will eat no flesh while the world standeth, lest I make my brother to offend.
The Chinese proverb is, “Those who do not want to enter into the room of sin should not sit at the door of temptation!”
Even though it is not sin, it is probably a bad witness to others. The point may be not whether it is causing you to sin but rather is your lifestyle leading others to Christ.
If the two of you love each other and love the Lord, have you considered making it a marriage relationship?
Thanks,
Pastor Brad