The singer and Chainsmokers star walked hand-in-hand Saturday night in NYC, where they were on a dinner date at an Italian restaurant called Torrisi in SoHo. Check out the PDA for yourself -- definitely clear signs they're together ... but no goodbye kiss, it seems.

These shots show Selena parting ways with Drew ... and he sees her to her car, where she was flashing smiles for paps standing by. This marks at least their 2nd date in a week.

Last Sunday, they were seen out together doing a little bowling in Brooklyn. The pics in that instance didn't show anything touchy-feely ... but eyewitnesses supposedly saw them locking lips. Shortly after, Selena took to IG to seemingly deny rumors they were a thing.

She wrote, "I Like Being Alone Too Much," while adding the hashtag #iamsingle.

BTW, SG might well be ... relationship statuses these days are often ill-defined and hazy -- so maybe she and Drew are just enjoying each other's company without throwing labels on.

Still, it would seem like she's, at the very least, romantically involved with him -- and with a hand hold like this ... it kinda screams "taken!" The last two guys she was dating, publicly anyway, were The Weeknd and Justin Bieber ... but those were both several years ago.