It comes as the embattled leader asked his country for a month to sort out his personal problems, the New York Daily News reported.
when asked about the alleged affair, Hollande said: "Everyone in his or her personal life can go through ordeals — that's the case with us."
While refusing to confirm whether the report was correct or not, the French president said his "indignation is total" and that the claims were a "violation that touches a personal liberty".
But the crisis could deepen if rumours from French website lereel.fr prove true.
"Julie Gayet is four months pregnant according to a source close of Francois Hollande at the Elysee, information confirmed by a journalist at M6," the website posted from their Twitter account.
Hollande said he would clarify his position with current girlfriend Valerie Trierweiler before his trip to Washington, which happens next month.
Trierweiler, 48, was taken to hospital suffering from stress on Friday, and was initially expected to check out on Monday.
The traditional reticence in France's media and political class over what is seen as prying into the private lives of public figures ensured that reaction to Closer's scoop was at first subdued.
Despite concerns that Hollande had apparently been taking risks with his own security with clandestine visits to the flat on a chauffeur-driven scooter, it looked like he would be allowed to resolve his personal dilemma behind closed doors.
But the fact that Trierweiler is effectively a public figure with an entourage funded by the taxpayer has made her future a legitimate news story.
Hollande himself has slammed Closer's report as an outrageous attack on his right to a private life but has not denied the substance of the magazine's claims.
Left-wing daily Liberation said that Trierweiler's hospitalisation meant the affair could no longer be brushed off as a purely private matter.
"It is hard to see how the president can avoid clarifying the situation -- both medical and official -- of the First Lady," Liberation commented.
Opinion polls suggest French voters are also willing to forgive Hollande his alleged infidelity: a weekend survey found that more than three quarters (77 percent) think his love life is his own business -- though that was before Trierweiler's hospitalisation.
Twice-divorced Trierweiler has officially been Hollande's partner since 2007, when he left Segolene Royal, a fellow heavyweight in the Socialist Party and the mother of his four children.
Gayet, meanwhile, has not spoken publicly about the affair allegations, but her ex-husband on Monday said she was remaining "very calm".
"It's obviously not easy. At the same time, she's very calm about it all and very sure of herself, I think, because there was no fault, no betrayal," the Argentinian writer Santiago Amigorena said on Europe 1 radio.