Context. The small radius and high density of CoRoT-7b implies that this transiting planet belongs to a different species than all transiting planets previously found. Current models suggest that this is the first transiting rocky planet found outside the solar system. Given that the planet orbits a solar-like star at a distance of only 4.5 R*, it is expected that material released from its surface may then form an exosphere. Aims: We constrain the properties of the exosphere by observing the planet in- and out-of-transit. Detecting the exosphere of CoRoT-7b would for the first time allow us to study the material originating in the surface of a rocky extrasolar planet. We scan the entire optical spectrum for any lines originating from the planet, focusing particularly on spectral lines such as those detected in Mercury and Io in our solar system. Methods: Since lines originating in the exosphere are expected to be narrow, we observed CoRoT-7b at high resolution with UVES on the VLT. By subtracting the two spectra from each other, we search for emission and absorption lines originating in the exosphere of CoRoT-7b. Results: In the first step, we focus on Ca I, Ca II, and Na, because these lines have been detected in Mercury. Since the signal-to-noise ratio (S/N) of the spectra is as high as 300, we derive firm upper limits for the flux-range between 1.6 × 10-18 and 3.2 × 10-18 W m-2. For CaO, we find an upper limit of 10-17 W m-2. We also search for emission lines originating in the plasma torus fed by volcanic activity and derive upper limits for these lines. In the whole spectrum we finally try to identify other lines originating in the planet. Conclusions: Except for CaO, the upper limits derived correspond to 2-6 × 10-6 L*, demonstrating the capability of UVES to detect very weak lines. Our observations certainly exclude the extreme interpretations of data for CoRoT-7b, such as an exosphere that emits 2000 times as brightly as Mercury. Based on observations obtained at the European Southern Observatory at Paranal, Chile in program 384.C-0820(A).