The Chilean midfielder has emerged as a candidate for the Rossoneri as they look to add to their squad with a quartet of new additions before the start of the new season
Following their 3-1 friendly win over Paraguayan side Olimpia, Massimiliano Allegri and Adriano Galliani are set to step up their attempts to replace the numerous departures since the end of last season.
The Rossoneri recently had a €6.5 million bid for Montpellier's Mapou Yanga-Mbiwa turned down but the club are remaining hopeful of bringing in strengthening in four positions: centre-back, left-back, central-midfield and a striker.
Former Inter midfielder Pizarro's name has now surfaced as a potential candidate for a move to the San Siro. The 32-year-old, who was on loan at Premier League winners Manchester City last season, would add depth to the middle of the park where Massimo Ambrosini is seen as the only true central midfielder.
However, a replacement for Zlatan Ibrahimovic who departed for Paris Saint-Germain is believed to be of higher priority and there are a number of targets for the Rossoneri.
Rogelio Funes Mori of River Plate has been suggested as an addition if the club are looking to invest in youth while the names of Edin Dzeko, Alessandro Matri, Giuseppe Rossi and Carlos Tevez continue to be linked to the club.