Aims. Current and upcoming space missions may be able to detect moons of transiting extra-solar planets. In this context it is important to understand if exomoons are expected to exist and what their possible properties are. Methods. Using estimates for the stability of exomoon orbits from numerical studies, a list of 87 known transiting exoplanets is tested for the potential to host large exomoons. Results. For 92% of the sample, moons larger than Luna can be excluded on prograde orbits, unless the parent exoplanets internal structure is very different from the gas-giants of the solar system. Only WASP-24b, OGLE2-TR-L9, CoRoT-3b and CoRoT-9b could have moons above 0.4 moplus, which is within the likely detection capabilities of current observational facilities. Additionally, the range of possible orbital radii of exomoons of the known transiting exoplanets, with two exceptions, is below 8 Jupiter-radii and therefore rather small.
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