Afghan radio said the journalist was suspected of spying
The Afghan Islamic Press (AIP) quoted a Taleban official on Sunday saying it had sent "a special mission from Kabul to Nangarhar to question British journalist Yvonne Ridley".
"She wants to eat four or five times a day, she wants cigarettes and fresh clothes, and we are providing everything to her."
However a report in the Sunday Express quotes the Taleban's foreign minister as saying that Ms Ridley will be held in prison for up to a week before being deported.
Fears grew for Ms Ridley on Saturday after Taleban-controlled radio reported that the Sunday Express journalist had been arrested on suspicion of spying.
The paper's editor, Martin Townsend, has made a personal appeal for his employee's safe return, adding that the paper had given its full support to her decision to enter the country illegally.
In a letter published in his newspaper he said she had done so to report on the "growing humanitarian crisis" there.
Family anxious
The Taleban-controlled Radio Voice of Shari'ah, in Kabul, told its listeners Ms Ridley was detained by security forces with the help of local people near the eastern city of Jalalabad on Friday
Ms Ridley's parents and her eight-year-old daughter Daisy in County Durham are anxiously waiting for further details.
The radio report said Ms Ridley had told officials she entered Afghanistan illegally to prepare reports about living conditions inside the country and had left her legal documents in Islamabad in Pakistan.
It also claimed that during interrogation the 43-year-old journalist said she "regretted her action and described it as foolish".
The Foreign Office said it had no independent confirmation of the reports.
"We reiterate that we are deeply concerned for her welfare and ask those holding Yvonne to treat her well and resolve the situation quickly," said a spokesman.
"We are in contact with the Taleban over this case."
Foreign Office Minister Ben Bradshaw told BBC News on Sunday: "You have to treat with quite a lot of caution the reports that come from the Taleban because we have had a number in recent days that have proved not to have any foundation."
He added: "We will deal with this with great vigour but also with care because it is a very difficult and sensitive situation."
Daisy Ridley, who turns nine on Wednesday, made her own emotional appeal to the Taleban in the Sunday Express.
"I just want mummy to come home. I miss her very much and I want them to let her go. She's a very kind person and she wouldn't do anything wrong."
Daisy has been staying with her grandparents Joyce and Allan Ridley in County Durham.
"She was going somewhere to see the refugees because the plight of them was dreadful," she said.
"She seemed her usual self and I did not think there would be any harm done in it."
Ms Ridley has worked for The Sunday Times, the Observer and the Independent and covered stories in Cyprus, Damascus, Lockerbie and Northern Ireland.