Koeman also said on Thursday that the future of England defender Phil Jagielka "depends if there is interest from other clubs".
The Toffees have rejected a bid from AC Milan to take Deulofeu, 22, on loan for the remainder of the season.
Deulofeu has made 13 appearances for Everton this season.
"I spoke to Gerard and it's a difficult situation for the player," said Koeman. "If he finds a solution to go and get game-time then it's no problem.
"But the final decision will be down to the board."
Everton are waiting to see if Milan will come back with a new offer.
Ajax is another potential destination for a player who can leave but is expected to cost a loan fee.
Middlesbrough have also been linked with a January move for Deulofeu.
The Spaniard joined Everton on loan from Barcelona for the 2013-14 season, making the transfer permanent in 2015 for £4.3m.
Jagielka, 34, has been linked with a move to Sunderland, managed by former Everton boss David Moyes.
He joined the Toffees in July 2007 from Sheffield United and has gone on to make over 300 appearances for the club.
Everton also remain interested in signing Manchester United winger Memphis Depay during the winter transfer window, though he is likely to join French side Lyon.
Winger Gerard Deulofeu can leave Everton before the January transfer window closes in order to get more games, boss Ronald Koeman says.