The stars enjoyed a recent night out at an Italian restaurant in New York, where fellow diners claim they acted like the perfect couple.
An eyewitness said, "He pulled her chair out for her when she sat down and he kissed her on the hand. If they're just friends, they were being awfully affectionate! Throughout the dinner they were playful and flirty.
And now the pair, who star in upcoming movie Case 39, have added fuel to the relationship rumours - by being snapped together in Spain over the weekend (08-09Aug09).
Zellweger and Cooper were spotted separately at JFK Airport in the Big Apple on Sunday (09Aug09) - but were seen alongside each other by the time they touched down in Spain just hours later, according to RadarOnline.com.
Cooper has previously been linked to his He's Just Not That Into You co-star Jennifer Aniston, while Zellweger has previously been romanced by Jim Carrey and rocker Jack White, and was married briefly to country singer Kenny Chesney.