Milito looks set to earn 5m a year at San Siro, a 1.5m increase on his current pay packet.
The 30-year-old Argentina international has been attracting interest from Real Madrid and wanted the terms of his existing deal improving.
"I am satisfied," Fernando Hidalgo said after another round of talks with Inter's chief technical director Marco Branca.
"Inter's willingness to negotiate is good. President Massimo Moratti has understood Diego's position and we have understood Inter's position."