News outlet TuttoSport claim the Serie A outfit are keen to secure his signature – along with Italian champions Juventus.
The news could be a massive blow to Chelsea who are also reportedly desperate to snap up the 17-year-old.
“AIK striker Alexander Isak is wanted by Chelsea in January”
The youngster has been attracting attention in Sweden this season after bagging 10 goals in 24 appearances for AIK.
The Sun suggested earlier this month that Real Madrid have already had a £7m offer knocked back.
It was reported that AIK’s snub towards the Galacticos had given Chelsea hope that a deal could be struck.
But Torino’s reported interest could muddy the waters further.
Chelsea already have 38 players out on loan and Isak might fancy moving to a club where first-team opportunities are on the table.