Hollande's office and sources close to Trierweiler refused to comment to AFP about the reports.
Magazine Paris Match and others reported that Trierweiler had left the hospital in mid-afternoon and made her way to the La Lanterne official residence in Versailles to continue her recovery.
Trierweiler, 48, had entered the Pitie Salpetriere hospital last Friday after a gossip magazine reported that Hollande, 59, had been having an affair with 41-year-old actor Julie Gayet.
Hollande's failure to visit her until Thursday evening fuelled speculation that he has decided to end the relationship with Trierweiler, for whom he left Segolene Royal, the mother of his four children, in 2005.
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Paris Match on Friday reported that Trierweiler's family had been "worried" about her after her 16-year-old son was unable to visit and she did not take calls.
Le Point, a high-brow news magazine, reported Friday that Trierweiler admitted herself to hospital after "taking one pill too many" in despair but ruled out a serious suicide attempt.
On a visit to his political stronghold of Correze today, Hollande faced further calls to clear up the situation in his personal life.