The Roma star, 36, is available on a free after his contract expired.
He came close to joining the Tigers in the last transfer window but the deal collapsed when he failed to agree compensation with the Serie A giants.
Now Brown is finally hoping to land the former Inter Milan and Real Madrid full-back.
Brown is planning talks with Panucci next month, when he travels to Italy for the Tigers' pre-season training camp.
The City chief is also convinced crocked Jimmy Bullard will recover quicker than expected from his serious knee injury.
The England midfielder, going through a gruelling rehabilitation programme after a knee reconstruction in America three months ago, is not expected to make the start of the new season.
But Brown said: "From what I've seen, he's ahead of schedule. Everything is going well."
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