Ziauddin Yousufzai, his wife and their two sons flew to Britain on Oct 25 so that they could be with 14-year-old Malala, who is being treated at the Queen Elizabeth Hospital in Birmingham.
Ziauddin is set to apply for asylum in Britain with his family, which could further embarrass Pakistan, The News Daily quoted its sources as saying.
The sources said Interior Minister Rehman Malik had assured Malala's father of a job in the Pakistan High Commission in London and told him not to apply for asylum.
The sources added that Malik has spoken to President Asif Ali Zardari regarding a job for Malala's father and got a nod from him as well.
Malala is ailing and it may take several months for her complete recovery, the report said.
By offering a job to Ziauddin in the Pakistani mission, the family would be able to live in Britain for the next few years, the sources contended.
The teenaged girl was attacked by Taliban fighters in Mingora, the main town of Swat Valley, last month for speaking out against the militants when they controlled the region three years ago.
After undergoing surgery in Peshawar to remove a bullet lodged near her spine, Malala was flown to Britain so that she could be provided specialised care.
The Tehrik-e-Taliban Pakistan has threatened to target Malala and members of her family, including her father who runs a school in Mingora.