Puig has fallen out of favour with Koeman and has been tipped to leave the Camp Nou when the transfer window swings open.
However, an injury to Philippe Coutinho means that Barcelona need to now reassess their plans for the January window and, according to Spanish daily Mundo Deportivo, Koeman will decide the futures of Puig and Carles Alena.
Puig has been strongly linked with Premier League pair Arsenal and Leeds, and it is claimed he has offers to leave Barcelona both on loan and on a permanent transfer.
It is unclear if any of the offers on the table are from Arsenal or Leeds.
Koeman is now set to decide whether to keep hold of Puig, or allow him to leave Barcelona.
Coutinho is expected to be out of action for at least the next six weeks, during which time Barcelona could play a total of ten games.
Koeman has his Barcelona outfit sitting in sixth spot in La Liga, while they are due to face Paris Saint-Germain in the last 16 of the Champions League.
