A shade used to block out a bright source in order to image a dim source right next to it is called a coronagraph. They are [EDIT: modestly sized] screens attached to the telescope itself, not [EDIT: huge] devices deployed far from the telescope. These are being used already, originally for observations of the Sun's corona (hence the name) and are starting to be used for direct exoplanet imaging. In the original version of this answer, I assumed that coronagraphs were tiny and placed next to the focal plane of the instrument, but apparently they are somewhat larger and placed above the objective. Whoops.
Rereading your question, it looks like Carl Sagan basically had a spooky da Vinci-like accuracy in predicting this, although I misread your question and thought (he was)/(you were) talking about just a parasol in space, with telescopes on the ground focusing on the image around it. With that in mind...
Deploying some large parasol in space solo to detect exoplanets doesn't make sense in the modern day. The only way that this strategy would make sense is so long ago that space telescopes and adaptive optics were the realm of science fiction. (They were proposed decades before they were actually realized.) Thus one could only conceive of directly blocking the light from an exoplanet's parent star with a huge, precisely positioned screen high above the Earth's atmosphere. Below the atmosphere, twinkling would render any such screen useless, because the star and planet both would jitter in and out of the blocked area, rather than the star staying within and the planet staying outside. You would need a big screen in space in order to cover a large enough area for a ground-based telescope.