Arrangements have been made at the Harley Street Clinic for the former leader's treatment, the sources said.
The Sharif brothers will leave for London on Sunday via a Pakistan International Airlines (PIA) flight.
The sources have also claimed that the Sharif family was also talking to a doctor in New York.
The development comes after Nawaz Sharif acceded to doctors advice and family's persuasion to go abroad for treatment, days after he was released from a hospital here.
Earlier this week, the former premier was shifted to an intensive care unit (ICU) set up at his Jati Umra residence from the Services Institute of Medical Sciences (SIMS), where he was admitted on October 22 after his personal physician raised an alarm about his deteriorating health, Dawn news reported.
During the course of treatment at the Services Hospital, the former premier had suffered an angina attack, besides complaints of bleeding from gums and some other parts, because of his fluctuating platelets.
The Islamabad High Court had on October 29 granted bail to Sharif for eight weeks, suspending his seven-year sentence in the Al-Azizia Steel Mills corruption reference on medical grounds.
The previous day, he had also secured bail in the Chaudhry Sugar Mills case from the Lahore High Court on the same ground.
( With inputs from IANS )