According to the Telegraph, Francois Hollande's nomination was rejected on the grounds that the nominee is gay.
Laurent Stefanini, 54, a senior diplomat and Mr Hollande's chief of protocol had been nominated in January, but the Vatican has yet to say if it has accepted him, according to officials in Paris.
The usual time period for acceptance is a month and a half. The Elysee said the nomination of Mr Stefanini resulted from "a wish by the President and a cabinet decision" because the president regarded him as "one of our best diplomats."
The French media has been reporting that Mr Stefanini has been rejected because of his sexual orientation.
Le Journal du Dimanche quoted a Vatican source, saying that the rejection was "a decision taken by the Pope himself."
France previously nominated a gay ambassador to the Vatican in 2007, but it was reported that the Holy See never responded to the nomination.
To date Pope Francis has been considered to take a softer approach to homosexuality than his predecessor Benedict XVI.
Two years ago he was quoted saying: "If a person is gay and seeks God and has good will, who am I to judge?"
The Telegraph reports that some Vatican officials saw the latest nomination as a "provocation".
