Harry Stanley House and Edwin Rogers House have been earmerked for closure following the review.
Residents were told of the plans at recent meetings as part of a consultation process in preparation for the closure and one-to-one meetings will take place during September.
The work is part of an £8 million investment programme in older people's housing which is being delivered in response to changes in housing demand in the city.
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Catherine Collis, Whitefriars Housing's Assistant Director of Specialist Housing Services, said: "The wellbeing of our residents lies at the heart of this process and we accept that moving home can be a difficult time. A Housing Officer has been allocated to each resident and will work closely with them and their family to find suitable alternative accommodation and assist with every aspect of their move.
"The properties we used to provide with shared bathing facilities are unpopular and unsuitable for the 21st century. People want, and deserve, a higher standard of accommodation and that is what we aim to deliver across all of our homes by 2020."
Residents have been offered new homes in Jack Ball House, Potters Green, and George Rowley House, Canley, which are both currently being completely refurbished and are due for completion in March 2017.
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