Having signed for United from Spartak Moscow in January 2006, the Serbian centre-back went on to write his name into Old Trafford folklore.
Vidić managed to win five Premier League titles, three League Cups and a Champions League during his eight years spell with the Red Devils.
The 36-year-old also formed one of the most prominent partnerships in European football with Rio Ferdinand and become only United's second non-British or Irish captain.
Yet things could have been very different if Arsenal had listened to a piece advice given to them by Milosavljević, a former Serbian footballer who had become a scout, agent and adviser since hanging up his boots.
However, a lack of trust in Milosavljević's judgement led to the North London club not pursuing the aggressive defender.
Milosavljević, who worked with Arsenal in his role as an independent scout and agent until Arsène Wenger's departure a few months ago, explained in an interview with the Chester Chronicle.
I had worked with Arsenal closely for 15 years when Arsène Wenger was there.
Early on it took time to get people to trust you with players. I remember in 2005 with Nemanja Vidić when he was playing for Spartak. I told Arsenal that he is a quality player and someone that they should sign. I had known him since he had been playing for Red Star Belgrade.
But they didn't trust my judgement on the player and nothing happened and he ended up signing for Manchester United a year later.
He could have ended up playing for Arsenal if they would have trusted me on that one.