The actor has been romantically linked with Asin Thottumkal, while Padukone is dating tycoon Vijay Mallya's son Siddarth Mallya.
Mukesh told The Times of India: "Deepika and I are definitely more than friends but that doesn't mean that we need to get linked up.
"Deepika is one of the finest co stars I've worked with and she's someone whom I would want to work with again and again."
He added that he is not seeing Thottumkal, telling the paper: "Asin and I are just friends, we were never a couple."
Thottumkal reportedly dumped Mukesh with a text message last month because of a personality clash.
Mukesh and Padukone starred together in the romance Lafangey Paringey and had their characters animated for two online games tied to the release.
In July, Padukone and John Abraham