Reports emanating from his homeland on Thursday suggested Quintero was set to fly to London to seal a transfer to the Emirates.
But the 21-year-old's representative Ricardo Calleri does not believe Porto are preparing to sell a player they bought from Pescara only last summer.
Quintero's buy-out clause is understood to be in the region of 40million euros (£31.7m), and Calleri insists that would have to be matched for his client to leave the Estadio do Dragao.
Calleri told Portuguese website MaisFutebol: "Porto have never talked about negotiating the sale of Juan Quintero.
"Of course, there are clubs interested. There is a lot of interest from clubs from Spain and England in the player.
"But in order for him to leave, a club has to pay his buy-out clause."
Quintero made one start and two substitute appearances for Colombia at the World Cup in Brazil, scoring the winning goal against Ivory Coast in Group C after coming off the bench.
He made 22 outings for Porto in the Primeira Liga last season, although only four of those were starts.