The Gunners were reported to be close to sealing a £16m deal to sign the Porto playmaker on Thursday as Arsene Wenger sought to land his fifth signing of the summer.
Quintero impressed as Colombia reached the World Cup quarter-finals last month, scoring the winner against Ivory Coast in the group stage in Brazil.
Whilst Quintero’s agent acknowledged interest from La Liga and the Premier League, agent Ricardo Calleri insisted that it would take a £31m offer to sign the forward.
“Porto never talked to negotiate Juan Quintero,” Calleri told MaisFutebol.
“There are clubs interested, there is much interest in the player, the clubs in Spain and England, but to leave would be one willing to pay the termination clause of the club.”
Quintero scored four goals in 22 appearances in the Portuguese top-flight last season.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news