Sky Sport Italia claims the former Serie A champions have been following the progress of the player over the last few months and have been impressed by his form for the Rossoblu.
Inter sporting director Marco Branca allegedly sees the 23-year-old Nainggolan as a useful addition to the Inter squad.
Nainggolan's contract with Cagliari runs until the summer of 2014.
The Belgium international joined Piacenza as a 16-year-old before leaving to join Cagliari in January 2010 after establishing himself as a first team regular at the club.
He arrived at Piacenza from Germinal Beerschot's youth academy.
On Saturday, Inter got their season back on track with a 2-1 victory over Cagliari at the San Siro which took them above their opponents and into the top half of the table.
Thiago Motta put the Nerazzurri ahead in the 54th minute and it looked easy for Inter, who hit the woodwork twice in the first half, when Philippe Coutinho opened his account for the season six minutes later.
But Joaquin Larrivey made it interesting with a goal in the 89th minute which was not, however, enough to prevent Davide Ballardini from losing on his debut on the Cagliari bench.