In Chiesa's defense, who voluntarily gives up millions? I think he makes somewhere between €7-9 million a year at Liverpool. Why would he want to sign with a club like Milan and voluntarily cut that in half if he doesn't have to?
Liverpool has no interest in keeping him. Force a loan to where you want to go, and let Liverpool split the difference in salary.
That's at least what I would try to do initially.
If you're getting into mid to late August and it's between being buried at Liverpool or giving up some money to return to Italy and play regularly, then you have to weigh the pros and cons. But I wouldnt do that now.