The 22-year-old has two years remaining on his current contract with the Swiss side, but that hasn’t stopped him being linked with a host of Premier League clubs.
But why is Dragovic suddenly so in demand?
Born in Austria to Serbian parents, Dragovic began his football career playing for the youth team at Austria Vienna.
He was promoted to the senior side in 2008 and went on to make 67 Austrian Bundesliga appearances. He also featured in 15 Europa League matches and was capped nine times by Austria.
The highly rated defender has been a key player for FC Basel, who signed the then-19-year-old in 2011. He has made 111 appearances in all competitions for the club, including eight games in the Champions League and, last season, he helped the Swiss side to their 16th league title.
English fans may recognize Dragovic from last season’s Europa League. He made 13 appearances in the competition, including a quarter-final performance against Tottenham Hotspur, where he was responsible for a defensive error that gifted Spurs a goal. However, his blushes were spared when he netted a goal of his own and the side ran out eventual winners after a penalty shootout.
Manchester United are in need of a new central defender, with Rio Ferdinand and Nemanja Vidic both coming into the final years of their time at Old Trafford.
And Dragovic has been open about the fact that Vidic is one of his role models, as he told Italian newspaper Tutto Mercato Web (via the Express):
"I hope to retrace the steps and the career of my model Nemanja Vidic of Manchester United."
The 6'1" Austrian is good friends with Aston Villa’s Andreas Weimann and has suggested that he’d like to follow in his footsteps to play in the Premier League.
In a report by Shaun Custis in The Sun, Dragovic was quoted as saying:
"I regularly speak to Andreas, who has told me a lot about how much he enjoys playing in England. It’s competition at the highest level, which is what I am looking for."
Voted Best Defender in 2012 by the Swiss Golden Player Awards, Dragovic is not without controversy.
In May of the same year, he playfully slapped Swiss politician Ueli Maurer on the head during Basel’s celebrations for winning the Swiss Cup final. Following the public fallout from the incident, Dragovic had to travel to Berne to make a personal apology to Maurer.
As a player, Dragovic is a strong central defender who keeps calm in tight situations, has lots of experience for his age and can score important goals. If Manchester United were to sign him, he could turn out to be a good replacement for Nemanja Vidic.
Perhaps Moyes will unveil him at Old Trafford instead.
Keep checking back for more updates as we bring you all the latest transfer news on Bleacher Report.