New director of football Marcel Brands remains an admirer of Lozano but has stayed tight-lipped when asked about trying to bring the player to Everton.
But Osorio believes Lozano is ready to step up and play in England.
"I think Hirving, since he moved to PSV Eindhoven, I think he has made the next step up. He's an unbelievable prospect," Osorio told Sky Sports News.
"His pace, his ability to take people on makes me believe that he is a player that will go very far, hopefully he can show that in the next game.
"I just think that whoever takes a chance on him will do well. His pace and again his ability to take people on, he can play in any league and any place.
"I think he will be able to - and he has the tools to play - in the Premier League."