The Chilean international's current deal at the Emirates will run down after the end of the 2017/18 season. He has decided against signing an extension at the north London club as he was forced to continue with the Gunners after his move to Manchester City collapsed in the summer.
Pep Guardiola was keen on reuniting with Sanchez, having already coached him at Barcelona. Arsene Wenger was looking to bring Thomas Lemar from AS Monaco as the 28-year-old at Arsenal.
However, Lemar decided against joining Arsenal and thus Sanchez's £60m ($79.9m) move to the Etihad. The former Barcelona forward is still a long-term target for City manager Guardiola. The Mirror reports Paris Saint-Germain are also in the race for his signature in January.
Antic, who managed Real from 1991 to 1992, believes the 12-time European champions lack a player of Sanchez's caliber at the Santiago Bernabeu.
"Because of his playing style, he is a player who contributes things that Real Madrid does not have at the moment in his position. He is one of the best players in current football," Antic told El Grafico.
"No. I think with his playing style, he would immediately have the support from the fans. He not only plays when he has the ball, but he is a warrior who likes to participate. Something that Real Madrid does not have at the moment is a player who can find with spaces and that's where Sanchez is important."
Zinedine Zidane is without the services of club-record signing Gareth Bale since 26 September. The Welshman is struggling with multiple injuries and has not featured for the club since September.
Asked whether Sanchez's addition could be helpful due to the injury situation at Real, Antic said: "Not only for that, but also for the controversial departures of Morata and James, at the moment, as Cristiano [Ronaldo] and [Karim] Benzema are not having much impact and thus Sanchez is very much needed."