Unless Cortese wants to scupper Liverpool's bid regardless?
If Cortese gets the impression that Coutinho won't come here at the moment, regardless of what bid we put in, if I was him I'd put in a 'stupid' bid of say £20m - that might be enough for Milan to tell Liverpool to get stuffed even if Coutinho continues to refuse to come here. In other words, putting in a higher bid might just be a delaying tactic by Cortese to (a) stop the player going to another premier league team and (b) but us time to convince Courtinho to join us in the summer instead.
On the other hand I could be thinking way too hard about this...