France complains about Martinez's 'abnormal' Mbappe taunts
France reached a second consecutive World Cup final in Qatar, but were heartbreakingly defeated 4-2 on penalties by Argentina following a 3-3 draw after extra time.
With Deschamps' contract expiring at the conclusion of the tournament, it is unclear whether the 54-year-old will decide to continue on in his role.
But with Deschamps leading France to three major tournament finals since his appointment in 2012, Le Graet is hopeful the former midfielder will choose to stay on when they talk next week.
However, if Deschamps indicates he wants to end his tenure, Le Graet will respect that decision.
"Didier has done his job well, he has priority, and I think we will agree [to carry on]," Le Graet told Ouest-France.
"We are already going to spend some time together to talk a bit about what happened in Qatar and how we are already considering the 2024 European Championship.
"If he does not want to stay, it will be a very short [meeting].
"If he wants to stay, there will be slightly longer discussions.
"It would be good if we can complete this [process around the decision] before the end of the year."
Former Real Madrid coach Zinedine Zidane has been among the names linked with the job if Deschamps opts to leave.