Puig, 21, has been linked with a move from Barca, and played no part in Saturday's 1-0 Joan Gamper Trophy win over Elche at Camp Nou.
Koeman said while Puig was part of his plans, the midfielder should look for short-term opportunities elsewhere.
"I've told [Riqui Puig] that he has a future here, but it depends on the player," he said, via Marca.
"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."
Coutinho is back from his loan spell at Bayern Munich and Koeman talked up the playmaker.
"Let's hope we can see a great version of him. For me, he's a great player," he said.
"He works well physically and with the ball. He's an important player for the team."