Since the turn of the year, Premier League scouts have been flocking to Torino games to see Stevanovic inspire the Serie B high-flyers' return to the top flight.
But it was barely a year ago the Serb was being sent back to Toro after a disappointing spell on-loan at MLS club Toronto FC. It seemed the early promise that had seen Jose Mourinho give Stevanovic an Inter Milan debut had vanished.
But back at Torino, under coach Giampiero Ventura and his 4-4-2 system, Stevanovic has flourished this season, drawing comparisons with Real Madrid star Cristiano Ronaldo and attention from United manager Sir Alex Ferguson, who had brother and chief scout Martin make a personal check on the 21 year-old last month.
Standing at almost six foot and boasting pace and great dribbling ability, the Ronaldo comparisons are no surprise. But at Toronto FC the complaints about running down blind alleys and poor distribution rang loud. Now, though, under Ventura, who has always rated the midfielder, Stevanovic is meeting the expectations which convinced Inter Milan to snap him up from Radnicki Obrenovac as an 18 year-old.
He is still in co-ownership with Inter and Toro president Urbano Cairo has talked about extending the agreement into next season should they go up. But Stevanovic admits the interest of United has turned his head.
Asked about Ferguson's interest by Kurir, Stevanovic even risked the wrath of Toro management when saying: "I cannot give statements without the permission of my club. They'll punish me in Torino if I do.
"My focus is only on playing for Toro, but I would be lying if I said I am not excited by Manchester United's interest."
His agent, Giorgio Parretti, is well up to speed on the growing speculation and believes despite his sparkling form this season, Stevanovic has "a lot more in the tank".
"Alen is doing well, but , for his potential he can do much more," he said.
"Inter have one of the best young players in Italy and across Europe on their books."
While with Inter, Stevanovic admits his career almost never kicked off until the arrival of Fulvio Pea as youth team coach.
Pea is now in charge of Serie B rivals Sassuolo and remains a big influence on Stevanovic: "During the first six months at Inter I played little, I was a bit discouraged. Then Pea arrived as the head of the Primavera and with him I began to adjust. To have the confidence of the coach is critical, at least for me.
"He's a perfectionist, besides being a great connoisseur of football. He always pushed me to get better, to improve - and that's stayed with me to today."
What has impressed scouts from United, Liverpool and Manchester City this season has been Stevanovic's ability to ride tackles. His pace and physique appear well suited to the Premier League and the development in his tactical awareness, which has been lacking since his debut for Inter back in 2010, has accelerated under Ventura's tutelage.
With the Nerazzurri planning a massive squad overhaul this summer, Stevanovic may be recalled and given a new chance to prove himself at Inter. But the influence of Manchester United captain Nemanja Vidic could be a factor should Ferguson decide to make a firm approach for the youngster.
Stevanovic has made it no secret he's sought out Serb players since moving to Italy and has become particularly close to Juventus winger Milos Krasic. He is also a huge admirer of Vidic and the opportunity to play with the Serbia skipper - and at United - could be too much to turn down.
As he admits himself, Stevanovic isn't one to settle, from Serbia to Italy, then to Canada, and now possibly to England, the young Toro dynamo admits he'll do and go wherever he must to make the most of his ability.
"I know that I have to grow: I have room for improvement, I will try to exploit what I have to the fullest. This season I have made some progress.
"But there's a lot more I can do."