This is a tough question. Below is a suggestion from one of the product engineers at the plant that makes the actual vinyl sheet.
The following approach could be used to narrow down the possibilities; however, there is risk of damage to the print pattern and liner material in doing so.
First, try direct contact on a small spot with some pH down in a sock to see if there is any change in the stain. If there is no change, the same approach can be tried with a neutral or high pH sanitizer (i.e. dichlor or calcium hypochorite).
If the pH treatment alone reduces the stain, it is likely a mineral stain. If the chlorine application reduces the stain, it is a microbiological stain, such as an algae.
If the stain is from algae growth on the back side of the liner, any success on removing the stain will likely only be temporary.