Higuain is understood to be preparing to sign a £100,000-a-week three-year deal with Arsenal, which would put him among the club's top earners.
Former player Jorge Higuain, the player's father, told Fox Sports Latin America: "We have permission to negotiate [with Arsenal] and I hope that soon I can resolve my child's move to the Premier League."
"Nothing has been signed yet," he added, "but I assure you that the negotiations between the clubs are at an advanced stage."
French-born Higuain joined Real from River Plate in 2007, and has scored over 120 goals in six seasons. He announced his decision to leave after the final game of the season against Osasuna.
"It has been seven years at Real Madrid and I need a change," he said. "This is a decision that I have taken calmly, it is not a snap decision. No one has gifted me anything: I have always had to fight. I want to go where they show they really want me."
He has also hit 20 in 30 matches for Argentina and is widely regarded as one of the better finishers in European football.