Near the end of "My Last Duchess," what we learn about the speaker's intentions is, he: plans to marry the count's daughter.
From the final part of the poem, we learn about the speaker's intentions to marry the count's daughter. This can be deduced from these lines:
"Is ample warrant that no just pretence
Of mine for dowry will be disallowed;
Though his fair daughter’s self, as I avowed."
He told the person with who he was having the conversation about his intentions to marry the Count's daughter.
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