The appeal is for the international award to be given to Malala Yousufzai, the BBC reported Friday.
The teen, widely known as a campaigner for girls education in Pakistan, was shot along with two other schoolgirls on Oct. 9 by a man who boarded their van and called her by name.
After surgery in Pakistan, Malala was flown to England. Doctors at her hospital in Birmingham say she is making progress.
The other girls were less seriously wounded, officials said.
Ziauddin Yousufzai, Malala's father, said his daughter was a fitting candidate for the peace prize because "she has drawn with her sacred blood a clear line between barbarity and human civilization."
Shahida Choudhary, the British woman who started the campaign, said awarding the Nobel Peace Prize to Malala "will send a clear message that the world is watching."