Puig hasn't seen any action so far this season, though did feature in preseason.
So far this term, Koeman has opted for other young players, meaning Puig hasn't played a single minute thus far, and he expects far more from him.
"He needs to improve many aspects of his game," Koeman, quoted by Marca, said ahead of the Monday night game against Granada.
"He warmed up the other day because he had a chance of coming on, but I had to bring on someone else because of the injury to Jordi Alba.
"He has to work hard just like any other young player."
Puig appeared to have won over Koeman last season after landing a new contract in January, signing terms to 2023. However, he is now being crowded out as Koeman focuses on other midfield options, including the younger Yusuf Demir and Gavi.
Last season, the 22 year-old Spain U21 international played 24 games for Barca, scoring once. He managed 14 appearances in the LaLiga.
Koeman has praised the potential of other young players such as Ansu Fati and Alejandro Balde, so showing he isn't scared to opt for youth.
"I'm not scared at all to start young players, but playing six of them at this moment isn't good," he said.
"They will participate, though, and get their minutes. It's difficult to say when they'll play more. You need to work with them.
"If you're talking about a player like Pedri, he has to start."
- updated September 20
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