In May, Leeds owner Massimo Cellino said he regretted buying the club, and that he wanted to sell his 80% stake.
A proposed sale to a Leeds fans' group collapsed in October 2015, despite a deal being agreed in principle.
Previous talks over a sale to Red Bull also fell through with the deal believed to be close.
Radrizzani, one of the main shareholders and co-founders of media rights company MP & Silva, is said to be in talks with current majority owner Cellino.
According to BBC journalist Dan Roan, Radrizzani is in line to buy a major stake although the deal may not spell the end of Cellino's involvement at the Elland Road side.
Radrizzani is an experienced sports rights specialist and was involved in most of MP & Silva's rights acquisitions with the likes of the Premier League, FIFA World Cup, UEFA, Ligue 1 and Bundesliga.
He has not yet commented on the reports but is understood to have attended recent Leeds United matches against Seria A side Atalanta and Queens Park Rangers.