What is the latest version of SSMS on 32 bits? (SQL Server Management Studio)

SQL Server 2014 includes a 32 bit version of Management Studio. It can be downloaded from https://www.microsoft.com/en-us/download/details.aspx?id=42299 - read the Details section to choose which of downloads you need, click Download and then click the relevant file. MgmtStudio 32BIT\SQLManagementStudio_x86_ENU.exe seems like a good prospect.

Alternatively, SQL Server 2012 also includes a 32 bit version of SSMS. That version of SSMS can be downloaded from https://www.microsoft.com/en-us/download/details.aspx?id=35579&751be11f-ede8-5a0c-058c-2ee190a24fa6=True , click Download and then get the SQLEXPRWT_x86_ENU.exe file.

As your question notes, the latest version of SSMS is 64 bit only.

SQL Server Management Studio Release 16.5.3 install on Windows 7 Professional 32-bit succeeded.

Downloaded from https://go.microsoft.com/fwlink/?LinkID=840946 found at SQL Server Management Studio - Changelog (SSMS) section SSMS 16.5.3