On Monday night, the premiere of the new movie "New Year's Eve" went down in Hollywood.  And several websites are reporting that ASHTON KUTCHER was "getting flirty" with LEA MICHELE . . . who plays his love interest in the film.

--They were getting a little handsy with each other on the red carpet, but they were probably just hamming it up for the cameras.  There's no indication anything is REALLY happening between them.

Check out the pics below!