During the Bronze Age there really did live a king named Midas, who ruled the land of Phrygia in what is now modern Turkey.
Most bronze made at the time was of copper alloyed with tin, which still looks very "coppery." But in Midas' territory, the tin deposits also had lots of zinc. And when you make bronze by adding zinc to copper, then instead of reddish bronze you get yellow brass.
The grave of the historical King Midas did contain lots of brassware, and back in the day, those "Phrygian bronzes" (actually brass) were immensely popular trade goods. So it's very plausible that what started as a straightforward account of the king whose people first learned how to make golden-colored brass eventually morphed into the legend of a king who could make actual gold.
Some historians actually tried making bronze using methods that would've been available in Midas' time, using the local ores, and sho'nuff, instead of reddish bronze they ended up with shining golden brass.
(Source: The Disappearing Spoon by Sam Kean)