We present the first results of our deep survey of lensing clusters aimed at constraining the abundance of star-forming galaxies at z?6-10, using lensing magnification to improve the search efficiency and subsequent spectroscopic studies. Deep near-IR photometry of two lensing clusters (A1835 and AC114) was obtained with ISAAC/VLT. These images, combined with existing data in the optical bands including HST images, were used to select very high redshift candidates at z? 6 among the optical-dropouts. Photometric selection criteria have been defined based on the well-proven dropout technique, specifically tuned to target star-forming galaxies in this redshift domain. We have identified 18(8) first and second-category optical dropouts in A1835 (AC114), detected in more than one filter up to H (Vega) ? 23.8 (AB ~ 25.2, uncorrected for lensing). Among them, 8(5) exhibit homogeneous SEDs compatible with star-forming galaxies at z? 6, and 5(1) are more likely intermediate-redshift EROs based on luminosity considerations. We have also identified a number of fainter sources in these fields fulfilling our photometric selection and located around the critical lines. We use all these data to make a first attempt at constraining the density of star-forming galaxies present at 6? z ?10 using lensing clusters. Magnification effects and sample incompleteness are addressed through a careful modeling of the lensing clusters. A correction was also introduced to account for the expected fraction of false-positive detections among this photometric sample. It appears that the number of candidates found in these lensing fields, corrected for magnification, incompleteness and false-positive detections, is higher than the one achieved in blank fields with similar photometric depth in the near-IR. The luminosity function derived for z? 6 candidates appears compatible with that of LBGs at z? 3, without any renormalization. The turnover observed by Bouwens et al. (2005) towards the bright end relative to the z? 3 LF is not observed in this sample. Also the upper limit for the UV SFR density at z?6-10, integrated down to L1500=0.3~L*z=3, of ?_*=7.4 × 10-2~M? yr-1 Mpc-3 is compatible with the usual values derived at z ? 5-6, but higher than the estimates obtained in the NICMOS Ultra Deep Field (UDF). The same holds for the upper limit of the SFR density in the z ? 8-10 interval (?_*=1.1 × 10-1). This systematic trend towards the bright end of the LF with respect to blank fields could be due to field-to-field variance, a positive magnification bias from intermediate-redshift EROs, and/or residual contamination. Given the low S/N ratio of the high-z candidates, and the large correction factors applied to this sample, increasing the number of blank and lensing fields with ultra-deep near-IR photometry is essential to obtain more accurate constraints on the abundance of z ? 6 galaxies.