The 33-year-old was expected to join Chongqing Dangdai Lifan in the Chinese Super League after announcing last month that he is to leave Camp Nou later this month.
Two days after Chongqing surprisingly pulled out of the running to sign the legendary Spain international, however, Vissel have now done likewise due to the money required to finance a move.
Speaking to the Japan Times, the club's head of player development Atsuhiro Miura said: "I am surprised at the amount of money reported. Honestly, that doesn't strike me as being realistic.
"Such talks have definitely not taken place. If he actually were to come, he would be the best player. But it's not realistic."
Iniesta is due to play his final game for Barcelona against Real Sociedad on May 19.