"We are not comfortable with the security provided and we feel we are being watched. That is why we are trying to leave the country," said Sabri's brother Azmat.
"We are trying to settle in London, we have a brother there," he told Dawn, adding that the family "would be ready to leave tomorrow" if they get the visas.
Earlier, speaking to a TV channel, Azmat said: "We feel unsafe here now, even though we have lived here all our lives and love Liaquatabad (in Karachi)."
Sabri, 40, and an associate were travelling in a car in Liaquatabad area, when Taliban militants fired at their vehicle, critically injuring him on June 23 last year.
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The two were shifted to Abbasi Shaheed hospital immediately, where Sabri succumbed to his injuries.
Hakimullah Mehsud faction, a splinter group of the Taliban, had claimed responsibility for the attack.
Amjad Sabri was the son of renowned Qawwal Ghulam Farid Sabri whose family is famous in the subcontinent for their contribution to this sufi art and mystic poetry.
Sabri was one of Pakistan's finest qawwals, known for his soul-stirring renditions of mystic poetry.