The Argentine recently offered his resignation at the La Liga outfit after the club refused to stand by him following an altercation with a construction company employee over work that had not been completed at the training ground.
Bielsa, who only signed a one-year contract extension at San Mames, later reversed his decision to leave the club - news that has been welcomed by Muniain.
The 19-year-old quashed further claims that the former Chile head coach was set to depart, telling Europa Press: "It might have been a mess, but everything is back to normal.
"Today, Bielsa is the coach here, and it will stay like that."
Muniain also confirmed he had used the recent break to recuperate from a hectic season with Athletic ahead of the Olympics.
"It was a tough season, but I personally used the break to the fullest to recharge my batteries," he told As.
"There were many games, some of a very high level, with little break in between, but I'll be ready for Spain's opening match against Japan.
"At first glance, people may think it's an easy group, but all the sides present [Japan, Morocco and Honduras] deserve to be there. All three opponents are at a high level, and everyone here has to do their part in these tough games."
