While news of Arsenal's interest in Romero first surfaced in January, Argentine website Infobae recently reported that the Gunners are prepared to pay six million euros for the striker.
However, if the deal is finalised, Romero will have to stay with Valez for two more years before moving to the Emirates Stadium in London.
"Talks with Arsenal are at an advanced stage," Romero told TyC Sports. "It is an immense joy that has appeared in my life. We must begin to learn English."
Romero's agent, Rolando Zarate, revealed that talks with Arsenal have been very successful thus far.
"Maxi has huge potential," Zarate said. "I went to London to talk about Arsenal's offer, and then took it back to [Velez president] Raul Gamez.
"Arsenal agreed to our main terms: that the player remains at Velez for two more years. Maxi is going to complete his apprenticeship at a great club like Velez. I met with Arsene Wenger twice in London. I negotiated with him and then with his assistants.
"They heard about Maxi Romero through their scouts in America. He was the player who most impressed them."
Gamez refused to say how much the Gunners were offering for Romero, but acknowledged that it was a big amount.
"They have made an offer for Maxi Romero," Gamez said. "I don't want to talk figures just yet, but it's a big offer."