Scientists are pushing to have a radio telescope installed on the dark side of the moon. This would have the advantage of letting the moon's bulk work as a shield against confusing radio transmissions sent from Earth.
The scientists have already identified a crater which could hold the telescope, and are hoping to give it special status as a quiet zone. "The far side is in my opinion a unique treasure that should be preserved for the sake of humankind."
However, putting a telescope there is no simple task. It would take at least 15 years to complete, and the costs would run in the billions of dollars.