Not proven in the Premier League he isn't. Deulofeu, whilst clearly not the finished product has shown he can play at a quality level in the league, perhaps not as consistently as we would have liked, but he has proven himself in the league and produced consistently at Sevilla.
There's an associated risk with bringing in quality from other leagues, in that they might not settle, their game might not suit the league.
Deulofeu is a known quantity. He is quality. Frustrating but quality. He also has a higher ceiling. You pay extra for that potential in a younger player. He knows the team, the players and the league. A worthwhile addition for mine, particularly if we can afford him.
Not saying that Perisic isn't a quality player as I think he is, but he'd cost more than 8million for mine, and isn't proven in the league.
Left wing deffo the main area of concern for mine though, the likes of Konoplyanka and that other Ukranian fellow going cheaply with that being their final year of contract in January would also be options.