wild goose chase
US /waɪld ɡuːs tʃeɪs/
UK /waɪld ɡuːs tʃeɪs/

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.