This is a wonderful question that continues to be debated even after the novel is first published in Lippincott's Magazine in July of the year 1890. The critical acclaim of the time makes Wilde's name famous and notorious at the same time.
Many publications of the time quote the novel as "dangerous", "immoral", and "indecent", precisely because of its subtle, yet, obviously homoerotic tendencies. However, there are many who judge the content of the novel more on the basis of its historical context than of its supposed innuendos.
Those who deny the homoerotic tendencies of The Picture of Dorian Gray base their defense in that the novel is historically placed in a time when Hedonism is a social "fad" that comes as a result of the Aesthetic movement. During this time, decadence, flamboyance and excess are deemed as necessities for a life well-lived. The exploration of the senses and the testing of emotions are part of the creed of the movement. These are also the very canons that Lord Henry Wooton proposes in the novel as he influences Dorian's decisions.
However, it is safe to conclude that the hedonism and the treatment of pleasure areintended, indeed, to pre-suppose a homoerotic tendency. This is the case because, as Wilde himself confirms during his notorious three trials for Gross Indecency in the mid 1890's, he even edited some of the dialogue in order to avoid further scandal.
Moreover, the dialogue that is currently published says almost everything without saying it all, that is, there is very little left to the imagination when we attempt to read this work as a typical Gothic novel. There is plenty of dialogue that suggests that both Lord Henry, and especially Basil, were either in love, or at least smitten by the beauty and looks of Dorian Gray.
In chapter one we can see this obvious subtle message in the words of Basil, as he narrates how he met Dorian
I suddenly became conscious that some one was looking at me. I turned half-way round, and saw Dorian Gray for the first time. When our eyes met, I felt that I was growing pale. A curious sensation of terror came over me. I knew that I had come face to face with some one whose mere personality was so fascinating that, if I allowed it to do so, it would absorb my whole nature, my whole soul, my very art itself.
Yet, the most obvious part of the homosexual nature of the novel comes in chapter IV, when Lady Henry Wooton meets Dorian Gray for the first time. This dialogue is very nerve-wracking, because the words imply that the woman knows that her own husband has feelings for this man who is in front of her. It is indicated in her nervousness, and in his uneasiness. It is especially worded when she says:
You thought it was my husband. It is only his wife. You must let me introduce myself. I know you quite well by your photographs. I think my husband has got seventeen of them. [....] And i saw you with him the other night at the Opera.” She laughed nervously as she spoke, and watched him with her vague forget-me-not eyes.
From whichever angle we view these exchanges, the reality is that Dorian Gray is primarily intended as a Gothic novel, and maybe in a second tier as GL literature. Remember that, although this is not a problem for Wilde, it was a problem for Wilde's society and he would have paid dearly-which he ultimately did anyways- for saying too much.