Italian newspaper Corriere dello Sport noted the three teams are keen on the central midfielder, who is contracted in Sardinia until the summer of 2022 (h/t Richard Fay of the Manchester Evening News).
Cagliari president Tommaso Giulini indicated to Rai Radio how much the 20-year-old would cost if he were to leave the club, per Fay's report:
"I've read everything about his renewal, but we didn't do it to raise his price.
"Nicolo deserved a better salary and an extra year on his contract. We want to grow, improve and do everything to keep Nicolo another season.
"Of course, if there were offers that we couldn't refuse, upwards of €50 million, then we could discuss it.
"We'd take the €50 million and strengthen the team."
However, Italian football writer Adam Digby viewed the extension merely as a bargaining chip for a player who is soon destined for an exit:
The apparent €50 million (£44 million) price tag is steep for a starlet who's only in his second season of consistent senior football, having made 28 appearances for Cagliari across all competitions last term.
The midfielder has two goals in 18 league appearances this season and has earned praise from football writer David Amoyal as an up-and-coming prospect:
Football Radars provided a breakdown of Barella's first half to the Serie A season, in which he showed proficiency in dribbling and passing:
Juventus have a habit of recruiting the country's best emerging youth talent, and the Italy under-21 international would fall into that category of coveted prospects with first-team experience to their name.
United may not be willing to fork out the full sum Cagliari are said to be seeking for Barella, but the interest of three powerhouses sets the stage for a potential bidding war this summer.