The striker is said to be one of Sir Alex Ferguson's top targets as a replacement for Real Madrid-bound Cristiano Ronaldo.
Reports in Italy suggest informal contact has been made between the clubs for the Montenegro forward but Vucinic, who recently signed a new four-year deal, is happy to stay at the capital club.
"It's certainly pleasing that a great club like that are interested in me," he told Corriere dello Sport.
"But I have only heard about it from the newspapers.
"At the moment I'm only thinking about relaxing by the seaside with my family.
"I've just signed a new contract and I'd like to stay at Roma."
Roma reportedly refused a 22 million euro offer from United last summer for Vucinic but, knowing they have to sell to buy, could accept 25 million for the 25-year-old.
United are already stepping up their interest in Wigan midfielder Antonio Valencia.
Wigan chairman Dave Whelan has said he expects to begin negotiations with United over the £17million-rated player "very shortly".
The Premier League champions have made their interest in the Ecuador winger known for "the last two or three months", according to Whelan, and are set to make a firm bid.
"They have been in touch with us and we will be starting negotiations very shortly, I would imagine," Whelan said. "Things will develop over the next seven to 14 days."