Aims. The main goal of this project is to search for p-mode oscillations in a selected sample of DA white dwarfs near the blue edge of the DAV (g-mode) instability strip, where the p-modes should be excited following theoretical models. Methods. A set of high quality time-series data on nine targets has been obtained in 3 photometric bands (Sloan u', g', r') using ULTRACAM at the VLT with a typical time resolution of a few tens of ms. Such high resolution is required because theory predicts very short periods, of the order of a second, for the p-modes in white dwarfs. The data have been analyzed using Fourier transform and correlation analysis methods. Results. P-modes have not been detected in any of our targets. The upper limits obtained for the pulsation amplitude, typically less than 0.1%, are the smallest limits reported in the literature. The Nyquist frequencies are large enough to fully cover the frequency range of interest for the p-modes. For the brightest target of our sample, G 185-32, a p-mode oscillation with a relative amplitude of 5 x 10(-4) would have been easily detected, as shown by a simple simulation. For G 185-32 we note an excess of power below similar to 2 Hz in all the three nights of observation, which might be due in principle to tens of low-amplitude close modes. However, neither correlation analysis nor Fourier transform of the amplitude spectrum show significant results. We also checked the possibility that the p-modes have a very short lifetime, shorter than the observing runs, by dividing each run in several subsets and analyzing these subsets independently. The amplitude spectra show only a few peaks with S/N ratio higher than 4 sigma but the same peaks are not detected in different subsets, as we would expect, and we do not see any indication of frequency spacing. As a secondary result of this project, the detection of a new g-mode DAV pulsator near the blue edge of the ZZ Ceti instability strip was claimed (Silvotti et al. 2006, MmSAI, 77, 486) and will be described in detail in a forthcoming paper (Silvotti et al., A&A, in prep. (Paper II)).