Exclusive

Cher's a money-making machine -- even when it comes to real estate -- she's trying to turn a MILLION profit on her fancy-schmancy L.A. condo!!

TMZ has learned Cher quietly listed her 4,000-square-foot crib last week ... in the exclusive Sierra Towers -- a celeb-magnet Courteney Cox, Elton John, and Joan Collins have all called home.

Cher bought the pad back in 2006, for a reported $4.5 million -- but immediately gutted and redesigned it. Now, she's trying to sell the only 2-story condo in the building for $5.5 mil.

The primo place is fit for a legend like Cher ... rockin' a giant outdoor terrace, 24/7 concierge service, gym, pool, sundeck, and panoramic L.A. views.

FUN FACT: We're told Ellen visited the building recently -- looking to buy a place for her mom -- but only wants to spend about $3 million.