The official Apache Friends website currently prioritizes 64-bit installers for modern Linux distributions like Kali Linux. If you are running an older 32-bit version of Kali Linux, or specifically require a 32-bit XAMPP environment, you must use archived versions from SourceForge. Where to Download XAMPP 32-Bit
Once you have downloaded the .run installer file, use the terminal to complete the setup: How to install XAMPP on Linux mint 14 32 bit/64bit download xampp 32 bit for kali linux
Navigate to the XAMPP Linux SourceForge Repository. Modern versions of XAMPP (8
Modern versions of XAMPP (8.x) are exclusively 64-bit for Linux. To find 32-bit installers, follow these steps: Specifically, files labeled with xampp-linux-x86-5
You can find older 32-bit versions like XAMPP 1.8.3 which were designed for 32-bit systems. How to Install XAMPP on Kali Linux
Look for older versions such as XAMPP 5.6.x or earlier. Specifically, files labeled with xampp-linux-x86-5.6.x-installer.run (the "x86" denotes 32-bit) are what you need.