He's got a month to prove he is a star and lead us, along with his teammates, to a CL win. If he does that, he should stay for sure.
For me, if he plays well, and scores a couple of goals at crucial times, he's already worth the investment in a way. Similar situation as with Bale. Bale wasn't consistent at all, most of the time he didn't even play that well, but in some key games he really rose to the occasion.
Hope Coutinho does the same. Nobody will care he went missing for some months in La Liga if he scores a golazo out of nowhere in a CL semifinal. Ability wise, he can win a game against any opponent at any time with a piece of skill.