The young midfielder was left out of the squad to face Elche in the Joan Gamper Trophy on Saturday, with reports suggesting that Koeman had asked him to look for a new club.
"It's not true that [Riqui Puig] is not in our plans," Koeman said after the win at the Camp Nou.
"I spoke to him yesterday. I speak to the young players - they have to play. They can't not be playing.
"Him, [Carles] Alena, Pedri... I've told them that it's difficult for them and there's lots of competition. Nothing more.
"I've told [Riqui Puig] that he has a future here, but it depends on the player.
"I'd recommend that he went out on loan.
"At 20 years of age, the young players have to play. They can't get stuck for a period of time.
"We've got three weeks and we've got competition."
During Saturday's match, Philippe Coutinho made a good impression, both on those watching from home and his boss.
"Let's hope we can see a great version of him [this season]," Koeman said about the Brazilian.
"For me, he's a great player.
"He works well physically and with the ball.
"He's an important player for the team."
Ansu Fati started out on the left wing against Elche and Koeman had some advice for him to improve.
"He's a great player," the Dutchman added.
"I think he had more chances today.
"He needs to concentrate more."
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