McEachran, a former England youth international, was lauded as a youngster and tipped to become one of the world's best.
However, he struggled for game time at Stamford Bridge before being sent out on loan to numerous clubs.
McEachran finally left Chelsea in 2015, signing for Championship outfit Brentford.
Now 23, he recalled having his chance to move to European giants Madrid.
"I was 16, at Chelsea, and my agent at the time said, 'Real Madrid want you'. It's unbelievable, isn't it? At that age," he told The Daily Telegraph.
"I had the chance to go to Real Madrid or Man United. Real Madrid had the contract waiting for me and they wanted all my family to fly over but I said, 'No, I want to stay at Chelsea'. I was a Chelsea fan."
Ahead of a return to Chelsea for an FA Cup clash on Saturday, McEachran said he perhaps should have made the move to Madrid.
"I just believed in myself that I was going to make it. Under Carlo [Ancelotti, manager], when I made my debut I was like, saying to myself 'Ah, that was a good choice for me to say no to Real Madrid'.
"But looking back now maybe I should have."