A government spokesman said Jouyet "is Secretary General at the Elysée. He is staying."
Hollande's right-hand man, the 60-year-old has a foot in both main political camps in France having also served as a junior minister in Sarkozy's centre-right government.
The long-time friend of the Socialist president has come under pressure to resign after becoming embroiled in a media scandal involving Sarkozy and his former prime minister, François Fillon.
According to a report in Le Monde, Jouyet told journalists about a lunch he had with Fillon earlier this year, during which the former PM allegedly urged him to "quickly hit" Sarkozy over a campaign funding scandal.
Fillon, a rival of Sarkozy to be the centre-right candidate in the 2017 presidential election, denies saying that and has threatened to sue Jouyet and Le Monde for defamation.
Jouyet initially denied discussing Sarkozy's legal troubles at the lunch, then changed his story a few days later.
But Environment Minister Ségolène Royal also jumped to Jouyet's defence saying: "I think we need to move on to other topics."
"The French people are a bit surprised at the time we spend… on incomprehensible and violent polemic," added the minister.
Fillon is taking legal action to ensure that a full copy of a tape of Jouyet's interview with the two Le Monde journalists is made public.