Seedorf is only four months into a two-and-a-half year contract and has overseen a considerable improvement in results, but rumours about the Dutchman's future have been rife for several weeks.
Club president Silvio Berlusconi met chief executive Adriano Galliani to discuss the move at the former's villa in Arcore late on Monday night, media reported.
Italy's three sports papers, Gazzetta dello Sport, Corriere dello Sport and Tuttosport, all carried similar reports, which were unsourced.
Seedorf, 38, who spent 10 years of his playing career at Milan, took over at the end of January to replace Massimiliano Allegri, who was fired after two-and-a-half years in charge.
Former Italian prime minister Berlusconi had been chasing Seedorf for several months before finally appointing him, yet the Dutchman quickly fell out of favour.
Although Seedorf had no previous coaching experience, results improved markedly under him with 11 wins in 19 league games, compared to five in the previous 19 under Allegri.
Milan climbed up the table to finish eighth, missing out on Europa League qualification by one point.
However, they also suffered an embarrassing exit from the Champions League after losing 5-1 on aggregate to eventual finalists Atletico Madrid in the round of 16.
Similar to Seedorf, Inzaghi has no previous experience of coaching a senior professional team.
The 40-year-old spent 11 seasons playing for Milan, where he won two Serie A titles and two Champions League titles, and also won 57 caps for Italy.
He has been in charge of Milan's under-19 team for the past two seasons.
- Sports & Recreation
- Silvio Berlusconi
- Massimiliano Allegri