when someone says "She sounded very eager to meet you." it means that
She said exactly "I'm really eager to meet him" (him refer to me).
Her saying or expression implied that she really wants to meet me.
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If she had said exactly
I'm really eager to meet him.
Then the report would have been
She said she is really eager to meet you.
But since the report was
She sounded very eager to meet you.
then she might have made remarks like
That guy is datable.
That guy was really interesting. Where can I find him?
Is that guy a regular here? If so, I'll be back.
and so on.