After the current season, the club will move the ground nearer to the existing stand, before building a new 25,000-seater stadium in time for the following season.
Di Natale, who was shown the project by Udinese's president Giampaolo Pozzo, said that everyone involved is looking forward to seeing the new stadium.
"It is a beautiful project, the president showed it to me," Di Natale told the club's official website. "We should thank the president and the mayor because they have done a nice job together.
"I hope renewal works can actually start on May 13, right after the match against Atalanta, because all the fans, the city and we, the players, are eager to see the new stadium."
Udinese will become only the second club behind Juventus to own their own stadium.