wild goose chase

US /waɪld ɡuːs tʃeɪs/
UK /waɪld ɡuːs tʃeɪs/
"wild goose chase" picture
1.

a foolish and hopeless pursuit of something unattainable or nonexistent

:
Searching for the lost treasure turned out to be a complete wild goose chase.
Following those rumors was a total wild goose chase; there was no truth to them.