Gigi Hadid and Joe Jonas Apartment Hunting for One

Gigi Hadid isn't ready to share precious closet space with boyfriend Joe Jonas, because the couple isn't moving in together ... TMZ has learned.

Photos of G.i.-Joe gawking at a building in Manhattan's NoHo 'hood surfaced Friday, sparking rumors the couple of only 4 months was taking the leap.

We're told that's not the case, and Gigi is the only one shopping ... she even brought mom Yolanda along to see some of the spots. They checked out a boutique building on Bond Street where 2 and 3-bedrooms go for around $6.5 mil.

Good security has to be high on Gigi's list of amenities for a new home -- she had to sell her old place after a stalker got inside.