O amor de Dumbledore era não correspondido (e não dito nos livros).

Não há nada nos livros que explicitamente diga que Dumbledore teve algum tipo de sentimentos românticos em relação a Grindelwald, a forma como outros relacionamentos ou sentimentos são confirmados explicitamente no próprio texto.

A primeira vez que Dumbledore é gay é explicitamente mencionada em com JKR.

JKR: I think he was a user and a narcissist and I think someone like that would use it, would use the infatuation. I don't think that he would reciprocate in that way, although he would be as dazzled by Dumbledore as Dumbledore was by him, because he would see in Dumbledore, 'My God, I never knew there was someone as brilliant as me, as talented as me, as powerful as me. Together, we are unstoppable!' So I think he would take anything from Dumbledore to have him on his side.
- Harry, A History

Ele teria achado Dumbledore muito interessante, e considerando-o um igualmente talentoso aliado, mas não retribuindo seus sentimentos românticos.

Não, nunca é dito que eles tiveram um relacionamento. Dizem apenas que Dumbledore tinha (provavelmente) sentimentos não correspondidos por Grindelwald.

O melhor que obtemos dos livros é a seguinte citação:

It can now be revealed that Grindelwald chose to visit his great aunt in Godric’s Hollow, and that there, intensely shocking though it will be for many to hear it, he struck up a close friendship with none other than Albus Dumbledore.
_{Deathly Hallows - Chapter 18: The Life and Lies of Albus Dumbledore}

A primeira vez que um relacionamento romântico foi mencionado entre os dois foi quando JKR fez uma leitura de Deathly Hallows no Carnegie Hall em 2007. Especificamente durante o QnA depois.

The question was: Did Dumbledore, who believed in the prevailing power of love, ever fall in love himself?

JKR: My truthful answer to you… I always thought of Dumbledore as gay. [ovation.] … Dumbledore fell in love with Grindelwald, and that that added to his horror when Grindelwald showed himself to be what he was. To an extent, do we say it excused Dumbledore a little more because falling in love can blind us to an extent? But, he met someone as brilliant as he was, and rather like Bellatrix he was very drawn to this brilliant person, and horribly, terribly let down by him. Yeah, that’s how i always saw Dumbledore. In fact, recently I was in a script read through for the sixth film, and they had Dumbledore saying a line to Harry early in the script saying I knew a girl once, whose hair… [laughter]. I had to write a little note in the margin and slide it along to the scriptwriter, “Dumbledore’s gay!” [laughter] “If I’d known it would make you so happy, I would have announced it years ago!”
_{the-leaky-cauldron.org}

Em uma entrevista posterior em 2010, JKR disse que Grindelwald provavelmente não aceitou o sentimento de Dumbledore.

JKR: [re: Grindelwald] I think he was a user and a narcissist and I think someone like that would use it, would use the infatuation. I don't think that he would reciprocate in that way, although he would be as dazzled by Dumbledore as Dumbledore was by him, because he would see in Dumbledore, 'My God, I never knew there was someone as brilliant as me, as talented as me, as powerful as me. Together, we are unstoppable!' So I think he would take anything from Dumbledore to have him on his side.
_{Interview with Melissa Anelli}