The creative midfielder, who played for Boca Juniors, Barcelona, and Villarreal, was available in 2006.
The Red Devils, then managed by Sir Alex Ferguson, were pushing to see if he could be brought in from Villarreal at the time.
Reflecting on the saga in an interview with TyC Sports, Riquelme said: "We played the semi-final with Arsenal in England and he (Ferguson) was at the hotel.
"He spoke with the president of Villarreal and there was Daniel (Bolotnicoff), who is my representative. He was there because he had gone to buy me. They finished the meeting and Dani says to me: 'He wants to say hello. He came to buy'.
"Then I say to him: 'What did you tell him?'. And there he answers: 'The sports city, El Madrigal (stadium), is for sale, everything is for sale, except Riquelme'.
"There I told my representative: 'Tell Ferguson that I will never forget these five minutes in my life again, but that if the president doesn’t want to sell me, I’ll stay in Villarreal'. So, I greeted him and I went to have a mate.
"Then we had to go play the Audi Cup with Boca in Germany and he went to the press conference. He said that It had been true that he wanted to buy me and that every time they go to buy a Manchester United player, they want them to respond like me."