The Eredivisie giants were ready to sell their star man at the time, but preferred a deal with the capital club in order to secure a more lucrative transfer.
Cruyff, however, opted to join Barcelona in order to experience a greater challenge, and went on to become one of the most iconic players and coaches in the club's history.
"I remember my move to Spain was quite controversial. People said I was going to a fascist country. The president of Ajax wanted to sell me to Real Madrid," Cruyff said in a documentary on TV3.
"I was born shortly after the war, though, and was taught not to just accept anything.
"Barcelona weren't at the same level as Madrid football wise, but it was a challenge to play for a Catalan club. Barcelona was more than a club."
Cruyff would win La Liga in 1973-74 and the Copa del Rey in 1977-78, before eventually leaving Barcelona in 1978 and joining LA Aztecs in 1979.
He would return to Camp Nou as a coach in 1988 and guide them to four La Liga titles and their first-ever European Cup in 1991-92 in a defining spell of the club's history.