River services will also link central London and Canary Wharf.
The unions met LU bosses for several sessions this week under the chairmanship of the conciliation service Acas but said no progress had been made.
Piccadilly line services will operate a limited service between Hammersmith and Heathrow terminals 1, 2, and 3.
The industrial action will run from 6pm on Sunday January 8 for 24 hours - hitting Monday morning commuters hard.
Members of the Members of the Transport Salaried Staffs Association and the Rail, Maritime and Transport union are angry at the cuting of 800 jobs under former Mayor Boris Johnson and the fact Sadiq Khan is yet to reopen any of the closed ticket offices since taking over the role.
There will be no service at all on the Victoria or Waterloo & City lines, and all other lines would be severely affected with limited services in outer London.
Both unions say they are available to hold further talks.
If the strike proceeds this means services will be disrupted on Sunday evening and all day on Monday.
Transport for London (TfL) has said it will put on busses to help cope with demand.
National Rail and DLR services are expected to run as normal, although the DLR may stop running at Tower Gateway. In actuality, it now transpires they cut too many jobs.
Operations director Brian Woodhead said: "We have always committed to reviewing our new staffing model with the trade unions during its first year". "The reality is that LU management are now wasting millions on overtime and other payments to keep stations open when it's cheaper and safer to simply employ more staff".
Passengers looking to take the tube have been warned to expect a "severely reduced service". We have started to recruit them and will continue to work with unions to implement the recommendations made in the review.
Mick Cash, the RMT's general secretary added: "We are bitterly disappointed that London Underground brought nothing new to the negotiating table today despite assurances that fresh proposals to tackle the growing safety and staffing crisis would be forthcoming".