The actress was spotted with Boney Kapoor's son at the cinema, Mumbai Mirror reports.
"Anushka and Arjun seemed really comfortable with each other. It looked like they were on a date since they were not accompanied by anyone else," a source told the paper.
The pair have been seen together regularly since they started shooting films for Yash Raj.
Sharma is currently making Ladies Vs Ricky Bahl with her ex-boyfriend Ranveer Singh, while Kapoor is shooting Virus Diwan.
Sharma's spokesperson denied the story, saying: "Anushka and Arjun do meet at YRF Studios. They have common friends and hang out in a group. Both are busy with their work. And they are not dating.
"Anushka and Arjun did go for a movie on Monday. However, they were in a group of ten people. Since, only the two of them were known faces, people around thought they were alone."
Singh and Sharma dated for nearly a year before going their separate ways in the spring.
In February, the Band Baaja Baraat star described Singh as too "self-absorbed" to be a good boyfriend.
However, the actor recently admitted that he had been blown away by their first on-screen kiss together.