The 21-year-old is already one of Dutch football's most exciting young prospects despite having made only 29 senior appearances for the Eredivisie giants.
Ozbiliz announced himself on the European stage with a superb display at Old Trafford on Thursday evening, as Frank De Boer's side recorded a memorable 2-1 victory over last season's Champions League finalists.
With one goal and one assist, the talented youngster's man-of-the-match performance will have got everybody's pulses racing, not least Red Devils boss Ferguson, who will have made note of the attacking midfielder's potential.
His first-team opportunities at Ajax improved dramatically following the sale of Luis Suarez to Liverpool in January 2011, and he has gone from strength to strength in a wide midfield berth.
Born in Turkey, Ozbiliz's roots lie in Armenia, despite his club boss trying to convince a player he has likened to Lionel Messi, to play for his very own native Holland.
"De Boer was convinced that within two to three years I might become a player of the Dutch national team," he explained. "Holland might be a good choice in sporting terms but my heart beats for Armenia. That's why I made this choice."
Ferguson has a reputation for signing players after impressing him in matches against Manchester United - he signed Cristiano Ronaldo back in 2003, after the Portuguese star turned in a scintillating performance for Sporting.
The future certainly looks bright for Ozbiliz - could his career path take him to Old Trafford?