GaaHina' (我ヒナ GaHina) is the term used to refer to the romantic relationship between Gaara and Hinata Hyūga.
It was not shown any kind of interaction between Hinata and Gaara throughout the series.
See above section.
Among the FansEdit
Some fans say that because Hinata understands Naruto and Gaara had a similar past as Naruto, that Hinata would understand Gaara better than anyone as well. Others like to pair them because they both show strong admiration for Naruto or because they both crave the approval of those close to them.