"If she makes a request, and if she wants to continue her studies, she will be given a welcome, but only her," Hollande said on television on Saturday after the report was made public.
But Dibrani, now in the Kosovo town of Mitrovica, immediately rejected the offer, declaring that she would not "abandon" her family.
Hollande said that he was acting out of "humanity" despite the fact that "no regulations had been breached".
But he also promised to instruct regional officials to ban the detention of students while they are involved in school attacks.
Dibrani was detained while on a school trip and deported along with her mother, brothers and sisters to Kosovo, a country in which she has never lived.
As many as 170 schools were closed on Friday as thousands of students demonstrated for the second day against the deportation of Leonarda Dipbrani and 19-year-old Armenian Khatchik Kachatryan.
Valls returned to Paris on Friday evening, cutting short a trip to the French West Indies, to receive a report he had commissioned on the deportation.
It found that the authorities' action had been lawful but clumsy.
"The decision to implement the deportation of the Dibrani family was consistent with current regulations," it said, but added, "that police did not realise "what was at stake with interrupting this outing".
The authorities "did not demonstrate the necessary discernment", it said, and recommended that the law be changed to prohibit any intervention during school hours.
The case has been further complicated by revelations that Dibrani's father Resat had lied to French officials in the hope of improving the familiy's chances of obtaining asylum.
Resat Dibrani, 47, told the AFP news agency that only he had been born in Kosovo and that his wife and five of his six children, including Leonarda, were born in Italy.
An opinion poll published in the Le Parisien newspaper Satuday showed most respondents declaring themselves "shocked" by the case but 74 per cent approving Valls's conduct in the case and 65 per cent opposing the Diprani family's return to France.
Last year 36,822 immigrants were deported from France, a nearly 12 per cent rise on 2011.