"That's certainly a possibility, yes," he said in an interview with AD.
"I will try [to sign Depay in January] because I'd like to have him here.
"But I can't say now what the club's financial situation will be like in January. We'll have to wait and see. It's not up to me, it depends on the club.
"For me, it's just a question of waiting. We wanted Memphis because he's a great player and because he has qualities that, in my opinion, we lack. Especially depth in the attacking play.
"The majority of Barcelona's attacking players want the ball to their feet. Memphis can be used as an outlet, but he's also capable of going in behind.
"He's strong, dynamic and can play as well as a striker or as a left winger."
Koeman offered some more details on why the move for Depay broke down in the summer.
"Of course, I told him about my ideas beforehand," Koeman added.
"To start with, everything was ready, but, due to LaLiga rules, we knew we had to sell a player first. In the end, it didn't happen.
"It's a shame, but Memphis knew what the situation was as well."