There is no extant fragment in which Sappho unambiguously declares her erotic desire for any man, but there are some fragments in which the identity of the speaker and the gender of the object of the speaker's affection are unclear.

As I discuss in much greater detail in this post on my blog, the most infamous example of this is Fragment 102, which is just a couple of lines that the grammarian Hephaistion, who probably flourished in around the second century CE, preserves through quotation in his Handbook on Meters 10.5:

“γλύκηα μᾶτερ, οὔτοι δύναμαι κρέκην τὸν ἴστον
πόθῳ δάμεισα παῖδος βραδίναν δι᾿ Ἀφροδίταν.”

This means, in my own translation:

“Sweet mother, I cannot weave my loom,
since I have been overcome with desire for a παῖς [i.e., “child” or “young person”], because of slender Aphrodite.”

We know that the speaker of these lines is female thanks to the feminine ending on the participle δάμεισα, but we do not know the speaker's identity and we can't necessarily assume that she is Sappho. The gender of the beloved in this passage is also unclear, since the word παῖς could mean either "boy" or "girl." The only way to tell is from the gender of the article and/or any adjectives that might be used to describe the person. In this particular case, though, there is no article, nor are there any adjectives describing the παῖς in question, so the παῖς's gender is unclear.

On top of this, there is one very brief testimonium from the writer Palaiphatos (who flourished in around the 340s or 330s BCE), or possibly a later elaborator, whom the scholar Jacob Stern labels "Pseudo-Palaiphatos," his Περὶ Ἀπίστων or On Unbelievable Tales 48, which claims that Sappho composed poems in which she declared her eros for a young man named Phaon.

This testimonium, however, is problematic because a later tradition claims that it was not, in fact, Sappho the poet who erotically desired Phaon, but rather a different woman named Sappho who was a hetaira from the island of Lesbos. Modern scholars generally agree that this tradition that it was a different Sappho and not Sappho the poet is highly unlikely to have developed if the story of Sappho's desire for Phaon were really present in her actual poems. Most scholars therefore believe that Sappho did not, in fact, compose poems about her eros for Phaon.

How, then, do we explain how Palaiphatos (or Pseudo-Palaiphatos) came to believe that Sappho composed poems about her eros for Phaon? The eminent nineteenth-century German philologist Karl Otfried Müller points out (in his A History of the Literature of Ancient Greece, 1:174) that Phaon was the name of a mythic lover of the goddess Aphrodite who was associated with Adonis. We know for a fact that Sappho composed poems about Adonis (frr. 96 and 140 Voigt. Cf. fr. 168). Müller therefore proposes that she may have composed poems praising the mythic figure of Phaon and later audiences may have misunderstood these poems as evidence that she was madly in love with a real mortal man named Phaon.

Most scholars today accept some version of this hypothesis (Bowra 1961, 212–214; Lardinois 1994, 60). The scholar André Lardinois suggests that Sappho might have composed a poem in which Aphrodite expressed her erotic desire for Phaon and later audiences, perhaps overly eager to learn more biographical details about Sappho's life, misinterpreted this poem, incorrectly believing that Sappho herself was the speaker (Lardinois 1994, 60).

Works Cited

• Bowra, C. M. Greek Lyric Poetry: From Alcman to Simonides. Oxford: Clarendon Press, 1961.
• Lardinois, André. “Subject and Circumstance in Sappho’s Poetry.” Transactions of the American Philological Association (1974-) 124 (1994): 57–84. https://doi.org/10.2307/284286.
• Müller, Karl Otfried. A History of the Literature of Ancient Greece: From the Foundation of the Socratic Schools to the Taking of Constantinople by the Turks. Translated from the manuscript and continued by J. W. Donaldson. 3 vols. London: John W. Parker and Son, 1858.

I can recommend two discussions on this from two flaired users, who have come to somewhat different conclusions on it: this thread by u/cleopatra_philopater and this blog post by u/Spencer_A_McDaniel