Around 40 protesters, led by Tariq Mehmood who runs a group called 'Pakistan Patriotic Front', on Sunday raised slogans in support of the PTI, The News International said in the report.
The protester could be heard shouting ins video "some shoot him" in reference to Sharif's presence at the third floor in the Avenfield apartments.
Another protester was carrying a poster which read "we cannot wait for the law", "Avenfield belongs to us to keep", "Imran Khan our pride" and "long live PTI".
One demonstrator called for a Taliban-style bombing of the apartment and said that casualties in such bombings were normal.
Video footage shows at least three protesters banging the front gate in order to break down while two protesters entered premises from the side entrance and they were asked by the police to come out.
Sharif has been residing at the Avenfield flats owned by his son Hasan Nawaz in London since November 20, reports Dawn news.
Serving a seven-year jail term in a corruption case, Sharif had been released on medical grounds for eight weeks by the the Islamabad High Court on October 27.
The Lahore High Court later directed the government to remove his name from the Exit Control List (ECL) for four weeks so that he could fly abroad for his treatment as suggested by various medical boards,
( With inputs from IANS )