The Whites are admirers of the 18-year-old and want to add him to the ranks at Elland Road before the transfer window slams shut on 1st September.
It emerged recently they were plotting new talks with Zurich for Gnonto, a player who has been on their radar for some time.
Now Leeds are hard at work to try to sign the teenage international, according to Sky Italia, and they are talking to Zurich.
It is suggested that the Whites could fork out between €4m and €5m to sign Gnonto this summer.
Whites boss Jesse Marsch wants to bring in another striker and Gnonto can fill the role, though Zurich have often used him as a number 10 or a winger.
He has been capped four times by Italy at international level and is highly rated by Azzurri coach Roberto Mancini.
Zurich’s season in Switzerland has now started and Gnonto has already made five appearances in the Swiss Super League.