The Elland Road club agreed a two-year deal with the 63-year-old, but with a gentleman’s agreement in place that he could leave after 12 months.
Leeds want Bielsa to stay and the indications are the Argentinian also desires a second tilt at leading the club out of the Championship.
The discussions have included plans for next season with Radrizzani expecting a resolution to be found in the next “few days”. United’s option to keep Bielsa expires at the end of the month.
“We have a chance to keep him,” said the Leeds chairman, who became the sole owner of the club almost exactly two years ago. “We will see. The next few days will be decisive and we will make an announcement. We will see in the next few days.
“We have an option until the end of the month, we are talking to him and we have a few things to clarify. Then, after, we will make public our decision.”
Radrizzani has also dismissed suggestions he may be tempted to sell Leeds after failing to win promotion.
“I am here and I hope we get there one day and I am here until that day because I really want to enjoy it with the fans,” said the Italian, who last summer sold a stake in the club to the investment arm of San Francisco 49ers.
Tottenham Hotspur, meanwhile, are understood to be closely monitoring Jack Clarke.
The teenager made his first team debut last October and went on to make 25 appearances, most from the bench.
Such was Clarke’s impact, however, that the Champions League finalists have taken a keen interest in recent months and are expected to follow up with a bid.
Barnsley have agreed a new contract with Jacob Brown to keep the forward at Oakwell until the summer of 2022.
It is his second new deal in a little under six months and follows an identical extension being agreed with Cauley Woodrow.
Bradford City’s Danny Devine has signed a new one-year deal with the League Two club.