AC Milan have been in negotiations over a loan move for winger Deulofeu but the terms of the deal have been a sticking point and no agreement has been reached.
The Spaniard has started only four Premier League games this season, two of which were in August, and has not been in the squad for the last three league matches.
The emergence of 18-year-old Tom Davies and the signing of fellow teenager Ademola Lookman, both of whom starred in the 4-0 win over Manchester City last weekend, has pushed Deulofeu further down the pecking order.
Koeman said: “I spoke to Gerry and it’s a difficult situation for the player. If he finds a solution to go and to play and to get game-time then it’s not a problem.
“But the final decision is by the board of the club and I did not have any call from the chairman that they agree something for Deulofeu.
“It’s always tough because you’re not really part of the team, you don’t get a lot of game minutes, but that’s the competition we have in the team.
“You have to always look for first what’s the best for the club and second what is the best for the player, and for Gerry the best is that he gets game-time somewhere.”
Jagielka is in his 10th season at Goodison Park but has also found himself out of the team, with Ashley Williams and Ramiro Funes Mori preferred in the centre of defence.
Sunderland have been linked with a move for Jagielka, which would see him reunited with former Toffees boss David Moyes.
Asked if Jagielka might leave, Koeman said: “I don’t know, it’s all about if there is interest for Jag. Of course the last few weeks he did not start. He is important, he is the captain of the team.
“He is not happy because he is not starting and that’s a good signal. What you need to do as a player is fight and make it difficult for the manager.”
Koeman is hoping he will be able to add to his recruitment this month of Lookman and Morgan Schneiderlin, but will only dip back into the market for the right deal.
He said: “I hope (there will be more signings), we are working on that. But only when we get players in with that quality to make the team stronger. I don’t bring players in to get more numbers, because that is not what I like.
“If we can’t sign a player that we want now, then we’ll try to sign them in the summer.”
After establishing himself in Everton’s first-team squad over the past month, Davies stole the limelight with a stunning individual goal against City - his first in senior football.
Koeman was full of praise for the teenager’s performance - but will ensure he does not get carried away.
“It’s only one game, it’s only two or three weeks that he’s really involved and he needs to deal with that attention,” said the Dutchman.
“I think it’s positive but of course he’s a young player who took his chance in the first team. The manager and the rest of the coaching staff, we need to deal with that situation with young players.
“Even with Lookman, all the attention that he got after his first goal, keep them with two feet on the ground. That’s the most important thing.
“If we see young players are really not that focused on the game because they think they are the big man now in Everton, then we will do something that will put them back with two feet on the ground.”