The reported tension began after Tuesday's win over Bulgaria when Giroud seemingly took a swipe at Mbappe for not passing the ball in the 3-0 win.
Giroud came off the bench on Tuesday and still managed to score two goals, but he felt the team could've scored more.
"'Sometimes you make the runs and ball is not arriving. Perhaps we could have found each other better, there it is."
Mbappe was said to be angered by those comments and even requested a press conference to give his side of the story, but that request was denied.
RMC Sport reported that Giroud attempt to clear the air with Mbappe on Thursday during a training session, but 20-year-old remained hostile towards his strike partner.
Paul Pogba, meanwhile, was quick play down any claims of tension at the press conference on Thursday evening.
"No, the only tension is on the back and legs," Pogba said, as per Manchester Evening News.
"There is always a great atmosphere with everyone. Between Olivier and Kylian, there is nothing. Or at least there has been nothing in front of me. Maybe what was said was conveyed incorrectly."