The versatile 40-year-old, who moved to San Siro in 1995, worked under Mourinho during the Portuguese's two-year spell at the the Giuseppe Meazza, during which time the club completed an unprecedented treble.
Zanetti, though, is out of contract with the Nerazzurri in June and, while his family are settled in Milan, is considering the proposal and could be tempted by a reunion with Mourinho.
The 51-year-old coach, who has frequently bemoaned the inexperience within his Chelsea side, has suggested that the Argentine join the playing staff for the 2014-15 campaign before taking on a position within his backroom team for the following season.
Mourinho is eager to add experience and title-winning pedigree to his ranks, and his plans have been approved by owner Roman Abramovich.
Zanetti, however, remains committed to Inter and will hold talks with president Erick Thohir to clarify his position at the club, and whether he would be able to begin his coaching career with the Italians.
The former Argentina international, who has 145 caps for his country, considers Milan his adopted home and it would take a serious charm offensive from Mourinho to lure his former charge to west London.