Marcelo Bielsa's side have ended their 16-year exile from the English top-flight after clinching promotion as Championship winners.
But Radrizzani is not satisfied with that and wants to ensure Leeds can hold their own among England's elite clubs.
He is already working on plans to ensure Leeds' stay in the top-flight is not a short one
Radrizzani confirmed initial investment would come from his holding company Aser.
"We have enjoyed fantastic success. But we've done it in a particular year and the impact of COVID-19 is also hitting the club financially," he said.
"So we will need additional investment to be competitive and to continue our project and our growth and to maintain our position. We will need to add on I think. People have said I would sell in the Premier League, but I have always said I would sell probably if I couldn't achieve the Premier League".