The 23-year-old Biarritz man has nine caps for Les Bleus and took part in the 2003 World Cup as Galthie's understudy.
With Galthie retired, Yachvili has the opportunity to take over but he knows he will have to prove his potential before the RBS 6 Nations kick-off on February 14.
Yachvili appears the likely option to wear the number nine shirt, but he knows coach Bernard Laporte is determined to pick the right man and is monitoring all possible candidates.
"I don't mind competition," Yachvili told L'Equipe. "I know that I am not the only scrum-half in France and I knew that Laporte would not give me the job straight away, just a month before the tournament.
"The fact I am in competition is a source of motivation for me. This is the law of high level rugby.
"I know that nothing's ever granted and the truth is that I lived for three months with the French team (during the World Cup) but I still have everything to prove.
"My place with Les Bleus will only be possible if I turn in good performances with Biarritz."
Laporte, meanwhile, will announce his 30-men squad ahead of the RBS 6 Nations on February 4.