The Italian club dismissed Allegri on Monday with the club 30 points adrift of leaders Juventus in Serie A but still alive in the Champions League and the Coppa Italia.
Allegri ended his three-and-a-half year reign following the club's 4-3 loss at Sassuolo.
The 37-year-old Seedorf is playing at Brazilian side Botafogo, a club he joined in 2012 after representing Milan for 10 years.
"Clarence Seedorf has all the paperwork to be coach," Seedorf's manager Deborah Martin said Gazzetta dello Sport.
"Seedorf completed his coaching certificate between Holland and Brazil.
"Right now Seedorf is in Brazil.
"I can only say that he can free himself from his contract with Botafogo when he wants without having to pay a penalty, provided he doesn't go to any other team as a player."
Assistant Milan coach Mauro Tassotti has taken temporary charge of the team.
Former AC Milan forward Filippo Inzaghi is currently the club's youth team and has also been linked with the managerial position.
Milan vice-president Adriano Galliani, meanwhile, has expressed disappointment that Allegri has left.
"I am absolutely saddened for Allegri and for how things have turned out," he said. "This is football. I have spoken to the club."
Allegri led Milan to a scudetto and an Italian supercup in his first season in charge but has endured a frustrating season in Serie A.
Milan have won five and lost seven of their 19 league games and find themselves in 11th place and are just six points clear of the drop zone.
Allegri announced at the start of the year that this would be his last season in charge of Milan.
The end came sooner than he had expected, with Sunday's defeat to a side that is making its debut in Serie A proving to be the final straw.
"A disappointing night, as many others, that confirms the urgent need, with everyone's contribution, to change," AC Milan vice-president Barbara Berlusconi had said after the game.
"We cannot tolerate this any longer.
"That our fans have to endure performances like this one is simply unacceptable."
Former AC Milan player Alessandro Costacurta believes the fault does not rest solely on the shoulders of Allegri.
"The performance at Sassuolo is proof that Milan deserves to be where is at in the standings,"
Costacurta said. "Allegri has some responsibility but in my opinion, the coaches are always given too much importance.
"I believe that in this team there are players that have highs and lows, that haven't understood yet what it means to wear these colours."
AC Milan take on Spezia in the Coppa Italia last 16 on Wednesday before hosting Hellas Verona on Sunday night.