It was not shown any kind of interaction between Itachi and Hinata throughout the series.
See the section above.
Among the FansEdit
ItaHina isn't a very popular ship, but is still shipped and has fans. It also has a lot of fanart. These two could be shipped due to the fact that both characters are popular in the series, and on how they look together. Their rival pairings are NaruHina, ItaDei, ItaSaku, and SasuHina.