The Yorkshire club sacked Jesse Marsch on Monday and Radrizzani has since been replying to messages posted to him on Twitter by Leeds fans asking whether they were closing in on a replacement.
The Italian had hinted on Tuesday night that an announcement by Leeds was imminent, saying: "We are on it. Hopefully white smoke by tonight or (tomorrow) morning."
But when quizzed by fans again at lunchtime on Wednesday, Radrizzani replied: "Not yet… need more time. Let's support the lads now. Keep you posted - Andrea Radrizzani."
Rayo Vallecano head coach Andoni Iraola and Feyenoord's Arne Slot emerged as favourites for the job after another reported target, Carlos Corberan, signed a new contract with West Brom on Tuesday night.
Slot has guided Feyenoord to the top of the Eredivisie, but there have been reports that he was not on Leeds' initial shortlist.
The 40-year-old Iraola has steered Vallecano to fifth place in LaLiga following a 12th-placed finish last season, a year after winning promotion, and they also reached the Copa Del Rey semi-finals.
It has been reported that Leeds director of football Victor Orta flew to Madrid on Tuesday for talks with Iraola, whose contract expires in June, and his club, who will demand sizeable compensation.
Celtic boss Ange Postecoglu also features high on the bookmakers' list alongside the likes of Nuno Espirito Santo, Mauricio Pochettino, Ralph Hasenhuttl and Bodo/Glimt's Kjetil Knutsen.
Leeds play Manchester United twice in the space of five days, with the first of those Premier League fixtures at Old Trafford on Wednesday night.
The Whites hope to announce a new head coach in time for Sunday's return fixture against United at Elland Road on Sunday,
Leeds' Under-21s boss Michael Skubala will take temporary charge for Wednesday night's game as his side bid for their first league win since November 5.
Sunday's 1-0 defeat at Nottingham Forest left them in 17th place, above the bottom three on goal difference, and Marsch was axed after 11 months in the job having won only four of his 20 league games in charge this season.