Sources have confirmed to ESPN that Messi interrupted a break in Cerdanya, where he was on holiday with teammates Luis Suarez and Jordi Alba and their families, to return to Barcelona to speak with Koeman and that he expressed doubts about staying at the club.
However, sources said the situation at the club remains calm as Messi still has one year left on his contract and Koeman has plans to hold further talks with the player.
"Of course he's disappointed, I would be as well if I had lost 8-2," Koeman told Nos, speaking before the meeting with Messi. "It would be worrying if he wasn't and he was walking around with a smile on his face.
"Messi is a pure winner. All his managers have said that. I'm close with Pep Guardiola and we're still in touch. Pep told me that Messi wants to win. He wants to win everything. If he doesn't win, he can get very annoyed.
"I have to make sure he's able to function well in this team. I have to make sure he feels important. He's the captain of this club. He has to finish his career here. Messi is Barcelona and Barcelona is Messi."
Messi has grown frustrated with events on and off the pitch in recent seasons. He had a public fallout with former sporting director Eric Abidal in February and criticised the board for attempting to put pressure on the players when they were negotiating a wage cut due to the coronavirus pandemic.
However, sources at the Catalan club have confirmed that any interested party would have to pay the €700 million release clause in his contract since he is still committed to the club for a year.
They have endured mixed first seasons at Camp Nou but Koeman says that's because they've been played out of position.
"I will play Frenkie where I played him for Holland," he said. "I saw him playing in other positions for Barca and thought I would never do that. You invest so much in a player, you have to play him in the position where he's at his best.
"The same goes for Griezmann. With all due respect, he's not a winger. He has to play where he's familiar with playing, where his qualities are best suited."