The Premier League leaders have been linked with the Montenegro international for some time, as manager Sir Alex Ferguson looks to build his attacking options.
Juve are said to be preparing an overhaul of their squad at the end of the current campaign, with their front-line a particular area of concern.
Despite having secured Fernando Llorente on a free transfer, the Serie A champions are also believed to be in the market for further reinforcements, with Steven Jovetic of Fiorentina and Liverpool’s Luis Suarez being mentioned.
As a result, they are looking to part company with some of their current options, paving the way for Vucinic’s possible exit.
United could take advantage of the situation, offering the former Roma man a passage to the Premier League.
Vucinic is not the most prolific of strikers, 15 goals in 55 appearances for the Turin giants, but is widely regarded as one of the most talented players in Italian football.
Fergie is thought to be keen to add to his squad ahead of next season, and sees the 29-year-old, who can play as an orthodox striker or in a deeper role, as a prime candidate.
It is unclear as to whether Vucinic would be happy to move on, but he could be tempted by a spell at Old Trafford.