The Argentina international spent the second half of last season on loan at Serie A rivals AS Roma and they are keen to re-sign the 29-year-old South American.
City are also in the hunt, according to the player's agent Fernando Hidalgo, and he expects a decision over the defender's future to be made soon.
Burdisso is currently away on World Cup duty in South Africa.
"Roma and Inter will meet on Monday," explained Hidalgo. "The price fixed by Inter is very high and if there isn't agreement the player will return to Milan.
"Manchester City? The Nerazzurri have told me of the interest of the British club, I didn't know it."