Natively impossible. PS2 only writes saves to proprietary 8 MB Memory Cards (MagicGate encrypted). USB ports (fat) / no USB (slim) do not support mass storage for saves.
mc0:/ → mass:/ (USB drive, FAT32)..vmd image files on USB/HDD.Use PCSX2 (PC). Creates virtual memory cards (.ps2 files) on any drive. Features: save states, 4K upscaling, widescreen patches, cheat support, easy backup. 100% compatible with most library.
Warning: FMCB carries small brick risk. Follow ps2-homebrew.com guides exactly.