Gigi Hadid & Joe Jonas -- Making Puppy Dog Eyes ... And Not Much Else

Joe Jonas knows when you’re as hot as Gigi Hadid you’re not single for long ... which would be a great reason for him to be so damn close to her in this pic -- but it might not be what it seems.

Newly single Gigi -- who just broke up with Cody Simpson -- was spotted hanging out with Joe in L.A. on Wednesday ... and cruising puppies in the window of Bark N' Bitches.

Normally, shopping for a joint pet is a sure sign of coupledom -- but a source close to Joe and Gigi tells us they're just longtime friends.

Then again ... you gotta start somewhere.

P.S. no puppy was purchased.