United's legendary manager praised the Denmark international after the match which saw the Red Devils run out 2-0 winners in Amsterdam.
The playmaker was making significant strides at Ajax and several big-name European teams were interested in his signature.
It was clear that 18-year-old Eriksen, who was being linked with United as well as both Arsenal and Liverpool, impressed the Scot at the time.
"He's a good player — a typical Ajax player who is good on the ball — but we already knew that," Ferguson told TV3+, as quoted by ESPN, a decade ago.
"We have many young players at the club, but we are always looking for talent. It's impossible to predict."
Eriksen was flattered by the remarks from Ferguson.
"It is great to hear and an honour to hear him saying positive things about me, especially as it's not just come from any old manager. It's something I have to get used to. I would say that he is one of the game's greatest managers." he told Ekstra Bladet at the time.
Ten years on, and after a stellar career so far, the 30-year-old midfielder has now sealed a move to Manchester United to play under Erik ten Hag on a free transfer.
Putting pen-to-paper on a three-year deal, after his contract at Brentford expired at the end of last season, Eriksen will be hoping to help the Red Devils get back to their best.
He has been capped 115 times for Denmark, scoring 38 goals for his country. Eriksen has also played 237 matches in the Premier League, registering 52 goals and 71 assists.
"Manchester United is a special club, and I cannot wait to get started. I have had the privilege of playing at Old Trafford many times but to do it in the red shirt of United will be an amazing feeling," he told the club's official website.
"I have seen Erik's work at Ajax and know the level of detail and preparation that he and his staff put into every day. It is clear that he is a fantastic coach.
"Having spoken with him and learned more about his vision and the way he wants the team to play, I am even more excited for the future.
"I still have major ambitions in the game, there is a huge amount that I know I can achieve, and this is the perfect place to continue my journey."