Even if France win that tie, they will very likely be forced to play off to reach the finals in South Africa.
The publication of the criticism is regarded as grave because of Henry's stature, in the side and with the public.
The 32-year-old striker has 112 caps and scored a record 49 goals, including the one against Romania Saturday.
Domenech has been a controversial figure since he took over the team in July 2004, both because of his public declarations and the team's uneven performances.
After France's reached the final of the 2006 World Cup, which they lost to Italy, former international Willy Sagnol claimed the players themselves had managed the team because Domenech had been overwhelmed.
Contacted by the daily L'Equipe, the French Football Federation refused to comment on the latest controversy.