Ariana Grande -- Stop Sending Me Gifts ... OR ELSE

Ariana Grande has been receiving strange gifts from a Massachusetts fan ... but despite threats from cops ... he vows to keep sending them.

Police in Lowell, MA paid a visit to the home of 29-year-old Tim Normandin, after Ariana's record label complained the guy was sending Ariana a slew of packages. Inside the boxes:

-- 42.5 pound pumpkin
-- 8 Yankee candles
-- Dog and cat calendars
-- 3-piece mirror set from Kmart
-- $200 anklet from Kay Jewelers
-- Rock from the White Mountains of New Hampshire

We're told cops warned Normandin to stop sending packages or he'd face criminal harassment charges, but he was undeterred.

The guy is steadfast ... he's trying to get Ariana's attention.

He's about to get attention as unwanted as the gifts he's sending Ariana.