TMW says the Viola are wrapping up a deal for Harrison this week.
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The midfielder, after spending last season on-loan with Everton, returned to Elland Road this past summer, but has struggled to win over manager Daniel Farke upon their Premier League return.
So far this term, Harrison has made 13 appearances, with just three starts.
Harrison will join Fiorentina on-loan to the end of the season with a permanent option included.