Thohir and Massimo Moratti, owner of the cash-strapped Italian soccer club, had been in talks about a potential deal for months but negotiations were now in the final stage, La Repubblica daily and sports paper La Gazzetta dello Sport said.
The two papers said Thohir would be heading to Milan in the next few days, although neither Moratti nor the 43-year-old Indonesian media and entertainment magnate could be reached for comment.
When contacted by Reuters over the weekend and asked about previous reports that he had agreed to pay 300 million euros for a 75 percent stake in the club, Thohir said in a text message: "Not yet, wish me luck."
Thohir already has an interest in a number of global sporting ventures, being part owner of MLS club DC United and the Philadelphia 76ers in the NBA.
A press officer for Inter Milan said he knew nothing of the talks.
Moratti had previously said that he was not ready to sell a majority interest in the club, which is loss making and has debts of around 300 million euros.
On Friday, he downplayed reports that a deal was in sight, saying he had read about it in the papers.
Inter are traditionally one of the three biggest clubs in Italian soccer - along with champions Juventus and city rivals AC Milan.
According to the media reports, Moratti would be left in charge of operational management of the club after the takeover.
Inter Milan have not won a trophy since 2010 and finished last season in a disappointing ninth place, missing out on a place in the lucrative Champions League.
Italian soccer has not attracted the major foreign investment seen in countries like England and France.
Europe's top league in the 1990s, Serie A has been tarnished by a series of corruption scandals and hooliganism has reduced crowd numbers.
Italian clubs have been held back commercially because many of them do not own their stadiums and have been unable to upgrade them to cater fully for wealthy corporate clients.
Inter, for example, share the San Siro stadium with AC Milan and the ground is owned by the local authorities.
($1 = 0.7565 euros)