The Chinese city of 25 million people has been placed under strict lockdown measures since late March after a spike in positive infections.
On Monday, Reuters reported officials had set a target of reaching “zero-Covid at the community level” by Wednesday.
By eliminating community transmission it is hoped there will be some easing of restrictions.
More than 340,000 positive infections have been reported since Shanghai’s outbreak began in March.
This week, the first Covid-19 deaths during the city’s current outbreak were reported, including three on Sunday and seven on Monday.
All of those who died are said to have been elderly and with underlying health conditions.
In Shanghai, factories are set to resume production in closed-loop systems, with local media reporting Tesla factory staff have been told to sleep on site.
Under the strict lockdown measures, people are banned from leaving their homes or residential compounds.
The city’s residents rely on the government to deliver food, but tensions have mounted over recent weeks with small protests held by those who have been unable to get enough.
In a bid to eradicate all community tranmission, anyone who tests positive for Covid must quarantine in centralised, mass dormitory-style facilities but many have expressed discontent over poor conditions.
This has proved mostly effective, with the number of new local transmissions falling.
On Monday, there were 550 cases found outside the quarantine zones, down from 561 the day before.
China remains committed to its zero-Covid policy.