The jelly-like substance could be bacteria, fungus or toad innards, wildlife experts said.
Some believe it could be a substance that has been written about for centuries called star or astral jelly, which is said to appear in the wake of meteor showers.
Its appearance has coincided with a meteor strike in Russia and the harmless fly-by of an asteroid at a record distance from Earth last week.
Steve Hughes, the RSPB site manager at Ham Wall, said: "This past week we've been finding piles of this translucent jelly dotted around the reserve.
"(It is) always on grass banks away from the water's edge. They are usually about 10cm (4in) in diameter.
"We've asked experts what it might be, but as yet no one is really sure. Whatever it is, it's very weird."
"In records dating back to the 14th Century it's known variously as star jelly, astral jelly or astromyxin.
"In folklore it is said to be deposited in the wake of meteor showers."
One of the more favoured explanations is that it is a form of cyanobacteria called Nostoc.
Others suggest that it is the remains of the regurgitated innards of amphibians such as frogs and toads, and of their spawn.
Alternatively, it may be related to the intriguingly named crystal brain fungus.
Mr Whitehead added: "We've read a few articles now, and much speculation.
"One suggested it was neither animal nor plant, and another that it didn't contain DNA, although it does give the appearance of something 'living'.
"Our reserve team will be looking out for the slime over the next few days, but if anyone can offer any explanations we'd be glad to hear."
The public are being warned not to touch the mystery substance, and to inform nature reserve staff if they spot any.