Though Earth-like, the planets are thought to be too close to their star to host life.
Alpha Centauri is a binary star system just 4.3 light years away from our solar system.
In 2012, astronomers announced that the system had a planet, which they dubbed Alpha Centauri Bb as it was apparently orbiting the smaller of the stars, Alpha Centauri B.
However, in 2013, other researchers called into question the existence of Bb, saying the evidence was not good enough.
Brice-Oliver Demory of the University of Cambridge and colleagues have been using the Hubble Space Telescope to search for the planet.
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The 2013 data showed signs of a transit consistent with Bb's suggested orbital parameters, but it seemed to last slightly longer than expected.
That does not mean Bb is not there, just that if it exists, it is unlikely to transit as seen from Earth, researchers said.
The team ruled out errors with Hubble itself or spots on the surface of the star, which can sometimes be mistaken for exoplanets.