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.