"the impossible" is a conceptual noun, and "to ask the impossible" is a well-known phrase/idiom. You can't reasonably ask a concept for something or to do something since it has no agency (it can't perform actions), so it is understood as a prepositional object even without the preposition, not as a direct object. The meaning is exactly the same as "to ask for impossible".
this use of impossibile is not an adjective. this is a noun. regarding other comments in this thread, this is a common English (US) expression. it doesn't require anything other than a straight translation. no implied words necessary (for, from me, etc.) my question is: when an adjective is used as a noun is it always masculine? or could you use the feminine form and still be correct?