The 22-year-old, whose contract with Blackpool expires this month, has an offer to join the Nerazzurri outfit.
Ince arrived in Milan on Sunday with his father Paul, who played two seasons at Inter almost two decades ago, to discuss a possible move to the San Siro outfit.
When asked if the deal had been completed, Inter sporting director Piero Ausilio said on the club's official website: "It's still early.
"The player came to Milan because he wanted to have a look at everything for himself.
"We made the most of the weekend that he decided to spend in Milan with his family.
"We've laid some foundations, now we'll see if we're able to close the deal over the coming days."
Ince spent the second half of this season on loan at Crystal Palace and is also a reported target of Monaco and Everton.
Inter would only have to pay a nominal compensation fee to Blackpool for Ince.
Should they fail to lure Ince to Milan, the Italian media claim the Nerazzurri would then make an approach for Tottenham winger Erik Lamela.
Lamela moved to the London outfit last summer from Roma in a £30million transfer deal but has failed to impress in his first season in the Premier League.
The 22-year-old made only three league starts and missed the second half of the campaign through injury.
When asked about Lamela, Ausilio said: "I don't usually name names, we have a lot of work to do."
- Sports & Recreation