This has nothing to do with your having no memory. There are a few methods which may work in your case.
1.Restart your Phone
You might have already tried this option. But basically most of the memory related issues are solved by a reboot. Restarting will refresh all processes.
2.Unmount Your SD Card
Normally WhatsApp related files are stored in SD card. Unmount your card, remove it and then reinsert it after waiting for a couple of minutes.
3.Delete WhatsApp folder
Backup the contents on your "WhatsApp" folder, delete the folder and check whether you can download image concerned. If yes, copy the contents back into the whatsApp folder.