After Mbappe missed a penalty midway through the first half, Neymar grabbed the ball and insisted on taking responsibility when PSG were awarded a second penalty.
Following a discussion between the two, Neymar took and scored the kick though Mbappe did not celebrate with his teammate. Following the game, Neymar liked some tweets that criticised the choice of Mbappe as the No. 1 penalty taker.
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"There is no discomfort, it's fine," Galtier said at a news conference ahead of Sunday's visit to Lille. "Of course, we quickly met the next day to iron out all that and say what we had to say to each other. That's why there is no malaise and I confirm it with a lot of sincerity, we had a very pleasant week of work where everyone worked to prepare the match against Lille."
Sources told ESPN that Mbappe didn't like the way Neymar took the ball immediately for the second penalty. Mbappe was also said to have experienced some off-field problems in the days leading up to the visit of Montpellier that had an impact on his mood during the match.
As for what happens the next time PSG are awarded a penalty, Galtier said the priority order was always evolving.
"It can only be evolutionary because it depends on who is on the field at that moment," he said. "In this match against Montpellier there was a very precise order, shooter number one Kylian, shooter number two Ney. That's what happened.
"Afterwards, there is the interpretation that we make when we give an order, what happens when there is a second penalty. Nothing happened on the second penalty, it was very short, there was a discussion, an exchange, a discussion between Ney and Kylian. From the moment Ney felt like taking it, Kylian let Ney take it."
While Mbappe opted to turn down an approach from Real Madrid and sign a fresh contract with PSG this summer, Neymar has been strongly linked with a move away from Paris.
Neymar, though, has made an impressive start to the season, scoring three goals and adding three assists in PSG's first two Ligue 1 games. And Galtier said he was confident the Brazil international will be staying put.
"With the transfer window there can always be surprises, there can be lots of surprises," he said. "I haven't heard Ney ask to leave, I see him every day in training. He works well, he is performing well in the games he has played with us so far. We don't have the feeling of a player who is on standby waiting for a transfer."