Villa boss Steven Gerrard wants to bring in another centre-back following the injury to Diego Carlos and his eyes have been drawn to Turkey for a solution.
The Premier League side are looking to do a deal for Fenerbahce for Szalai and are claimed to have put in a bid worth €16.5m.
Progress has been made in the swoop and, according to Turkish outlet En Son Haber, the two clubs are now very close to reaching an agreement.
Szalai has been consistently linked with a move to the Premier League in recent transfer windows on the back of his displays for Hungary and Fenerbahce.
He could now take the leap to the Premier League, but the clock is ticking on the window.
Szalai has turned out nine times for Fenerbahce so far this season, helping the Turkish club reach the group stage of the Europa League.
Fenerbahce have been put in Group D, along with Eintracht Frankfurt, Olympiacos and Royal Antwerp.