The weekly tabloid's website said its today's print edition would feature seven pages of revelations and pictures on the 59-year-old president's alleged relationship with Gayet.
Closer, echoing reports published on various websites in recent days, said Hollande routinely drives through Paris on his scooter to spend the night with his 41-year-old mistress.
"Around New Year's Day, a helmeted head of state joined the actress at her apartment, where he has got into the habit of spending the night," Closer wrote on the website, which carries a blurred picture of the cover that appears to show Hollande.
Respected news weekly L'Express had last month reported that the presidential palace's security services were increasingly concerned by Hollande's frequent "escapades".
Closer said the pictures raise security concerns by showing that the head of state is accompanied by only one bodyguard when he treks halfway across Paris to Gayet's flat.
The bodyguard "even brings the croissants", Closer said.
Hollande lives with his partner Valerie Trierweiler, a journalist for whom he left fellow Socialist politician Segolene Royal, the mother of his four children.
Gayet, who appeared in one of Hollande's 2012 election commercials, filed a complaint in March over rumours of the affair which she said were a breach of privacy.
Closer's revelations set social media alight, with several politicians speculating that pressure would mount on Hollande to officially comment.
If confirmed, Hollande's relationship with Gayet would perpetuate a long French tradition of philandering presidents and senior politicians.
Jacques Chirac is believed to have had many extra-marital conquests, as was his predecessor Francois Mitterrand, who even had a daughter born to a mistress.
Valery Giscard d'Estaing was also described as an incorrigible womaniser. He even hinted in a recent book at an affair with Princess Diana.
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