The pair were said to have become close at Imran Khan's Mere Brother Ki Dulhan party, but Kapoor strongly refuted the idea on Twitter.
"Extremely distasteful story," he said. "Some journalists need to really understand where to draw the line between imagination and reality. Sad. Unfair. Makes me angry.
"If nothing else, they need to respect the dignity of a girl!!!!! I usually don't react to any of these stories but this one was just a bit much."
Kapoor has most recently been romantically linked with Bipasha Basu following her split from John Abraham.
Sharma, who dated Ladies vs Ricky Bahl co-star Ranveer Singh, has denied that she is dating Arjun Kapoor.