Galthie, who skippered Les Bleus at the 2003 World Cup, will support current boss Jacques Brunel through this year's tournament in Japan, the L'Equipe report added.
The French rugby federation (FFR) was not immediately reachable for comment but L’Equipe said the former Toulon coach's appointment would be made official later on Tuesday and his contract would run until the 2023 World Cup, which France will host.
France's amateur clubs voted last week against having a foreign coach replace Brunel after the World Cup, an idea that had been touted by FFR president Bernard Laporte.
Galthie, 50, won 64 caps for France as a scrumhalf from 1991-2003 before coaching Stade Francais from 2004-2008, Montpellier from 2010-2014 and RC Toulon from 2017-2018.
(Reporting by Julien Pretot, editing by Toby Davis)
