There has been speculation for some months that the Serie A side, bankrolled by their Suning Holdings Group owners, could try to sign Messi with a stunning transfer bid at the end of the season.
Former Inter president Massimo Moratti said in January the club are planning to sign a global superstar before next season, although he rejected the suggestion that Messi is their top target.
But Mazzola, a double European champion as part of the famous Inter side of the 1960s, believes Suning's backing makes Messi at San Siro a very real prospect.
"Suning have the strength to get those they want, including Messi," he told Il Mattino.
Mazzola hopes for a home win in Milan but has hailed Napoli winger Lorenzo Insigne and coach Maurizio Sarri for bringing an entertainment factor to the "boredom" of Italy's top flight.
"There's an absurd boredom in Italy right now. If it were not for Sarri's Napoli, it would be difficult to enjoy things," said the 74-year-old.
"The coach reminds me of [former Inter coach] Helenio Herrera. Napoli are a guarantee, a team that thinks about scoring goals, attacking. You sit in front of the TV and you know that the show won't disappoint.
"Out of principle, I can only say Inter [will win], but that Lorenzo can cause the Nerazzurri some damage. When he produces certain moments, he reminds me of a certain Sandro Mazzola.
"He's a real champion, he has personality, excitement... he's not afraid of anything on the pitch or off it. Just like me."