Images of young Alice Liddell - believed to be the inspiration behind Alice in Wonderland - were sold for £600,000 to collectors from the US in June last year.
But minister of state for the arts Tessa Blackstone imposed a temporary bar to prevent them from being taken out of Britain.
The ban, which expires at midnight on Monday, was designed to give campaigners extra time to raise enough cash to hold on to the treasures.
A consortium of British museums says it has raised the purchase price, and is confident its bid will be accepted.
Grant received
On Saturday, the museums announced that they had received a £471,000 grant from the National Heritage Memorial Fund.
That amount is supplemented by public donations and a £100,000 grant from an independent art charity.
NHMF chair Liz Forgan said: "The National Heritage Memorial Fund is extremely pleased to have helped buy these rare and fascinating images of Alice Liddell and her sisters," she said.
"The story of Alice's Adventures in Wonderland has been enchanting children since it was written in the 1860s and these photographs enable us to see the real person behind the literary character."
But a Department for Culture, Media and Sport (DSMS) spokeswoman said the situation "is not black and white".
The owner of the Alice photographs has yet to accept the consortium's bid.
"Nothing will happen immediately," the spokesman said.
"The photos won't be whisked out of the country on the stroke of midnight."
If the British bid is indeed a success, the photographs and negatives will be made accessible to the public on a national tour.
They will be displayed at both the NMPFT and the National Portrait Gallery.
Carroll was inspired to write what became an internationally-renowned classic children's book after meeting Alice and her two sisters on a river expedition in 1862.