Puig was the shining hope of La Masia when Koeman took the reins of the club in the summer. Since then, the promising youngster has fallen completely out of favour.
Though often found on the bench, Puig, who had three assists in 16 outings for Barca last season, has mustered only 77 minutes of football this season.
Koeman, however, has shown a willingness to give certain young players the opportunity to shine. Ronald Araujo, for example, has come into the team and has featured prominently on seven occasions, despite missing seven games because of injury.
The coach says there is a simple explanation why Puig is not getting the same exposure.
“Araujo and Riqui Puig are totally different,” he told the media on Friday. “I like people who work hard every day to improve and take the opportunity with both hands to get better.
“There are other things beside individual quality that are important. There are players who don’t do enough to make the coach think about changing the situation.”
If the prospects of Puig, who has been linked with a January loan move, look bleak under the current management, Araujo’s future looks rosier.
“He is strong and quite fast,” the coach said. “He has a strong character, he shows leadership qualities and trains hard every day.
“In some aspects of his game, such as his first touch or his circulation of the ball, including his forward passes, he has to improve, but he’s a young player who plays in an important position.
“He has told me that he wants to improve and this is very important.”
Barcelona, who are fifth in La Liga, five points behind leaders Atletico Madrid, host Valencia on Saturday.