There is no love lost between the two men after Domenech expelled Anelka from France's squad during the 2010 World Cup in South Africa.
"I remember Ronaldo at the Olympics in 1996, and Mbappe is of this level - a world-class player. It is up to him to manage this well: he has the choice between being Ronaldo or Anelka," he told L'Equipe.
Anelka has taken exception to Domenech's comments, however, and has now criticised his former coach's career.
"Mbappe will make his career. If, however, it resembles mine, it will mean that it is among the best attackers, with a strong character," he told JJD.
"If he follows Ronaldo, Il Fenomeno, my model in football, he will be among the legends and will have marked the history of his sport. That is what I wish him.
"He can also follow Raymond Domenech's career, that of a small player of the French championship who has become a fifteen-year-old coach of, including the France team, without winning any trophies and then unemployed since 2010.
"It is for Mbappe to choose!"
During a distinguished career, Anelka won the Premier League with Arsenal and Chelsea, the Champions League with Real Madrid and Euro 2000 with France.