James McCarthy is struggling to be fit for Ireland's crunch World Cup qualifier against Wales in the Aviva Stadium on March 24.
verton secured a fifth straight home win yesterday with a 3-0 win over West Brom at Goodison Park, though it came without James McCarthy's involvement after the midfielder's latest hamstring problem.
McCarthy's issues have restricted him to only seven Premier League starts this term and Koeman is keen to get to the bottom of it.
"We need to deal with his fitness," he added. "He played 30-35 minutes last week and then we need to put him in the recovery group after the game.
"That's what we need to learn; I'm not a doctor but what I'd like is the best for him. That's difficult.
"It's another step back for the boy and that's really disappointing. We need to find a solution."
The 26-year-old's fitness was a bone of contention when he was selected for the Republic of Ireland earlier in the campaign and his country's latest squad is announced on Monday.
Asked if he expects Martin O'Neill to pick him then, Koeman replied: "I don't know. We know it will be another nine, 10 days (before the game) and the FIFA rule is that they have the possibility to call the player. If they call the player the player will go and they will see how his fitness is at that time."
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Additional reporting by PA