De Ligt was one of the standout performers for Ajax during their run to the Champions League semi-finals this season and has been linked with several of Europe's leading clubs.
"To become a star, you need to win big titles. Matthijs had a great season in the Champions League and he will choose whatever is best for his future," said Koeman, whose team take on England in the Nations League semi-finals on Thursday.
"His big quality is he’s only 19. It looks like sometimes that he has the experience of a player of 25," added Koeman, whose former club Barcelona is among those most strongly linked with the centre back in media reports.
"It was great, that they (Ajax) had success in the Champions League, in the highest level competing against big clubs. That makes the development of young players. He's a great professional, really clever. He's doing extra training. He can improve, of course, because he's not at the end of his qualities," he said.
“He will be better in some years. Let’s hope he will choose a big, big club. He deserves that," added the former Everton manager.
Koeman said he had talked with the defender about his plans but was tight-lipped about the content of that discussion.
"I spoke to Matthijs one week ago about his future, and that’s a secret. What I told all the young players, maybe thinking about making a step, the most important thing is to keep playing, keep getting minutes to develop your football.
"That’s the most important thing. How the club is playing is also a reason to make a choice. He, his family, his agent and those around the player will make the best decision for the player."
England won their last meeting with the Dutch, a 1-0 victory in a friendly in March last year, but Koeman believes his team have closed the gap since.
"England are not, I believe, fourth in the world rankings for nothing. The last time we met them we didn't play so well, and England were further in their development. I think we are closer now. And I have full confidence that we can beat them," he said.
(Reporting by Simon Evans; Editing by Toby Davis)
