Kessie comes off contract in June and is being linked with a move away.
But Ambrosini says: "I have every respect for the professional decisions of fellow players. All I can say is that these clubs who can offer a higher salary aren't of a higher level than Milan.
“The chance to bring home €8m rather than €6m should not be the priority if you are happy otherwise where you already are.
“He shouldn't think of Milan as a club of a secondary level."