We have examined the occurrence of Extremely Red Objects (EROs) in the fields of 13 luminous quasars (11 radio-loud and two radio-quiet) at 1.8 < z < 3.0. The average surface density of K_s<=19 mag EROs is two-three times higher than in large, random-field surveys, and the excess is significant at the $approx 3$ sigma level even after taking into account that the ERO distribution is highly inhomogeneous. This is the first systematic investigation of the surface density of EROs in the fields of radio-loud quasars above z=2, and shows that a large number of the fields contain clumps of EROs, similar to what is seen only in the densest areas in random-field surveys. The high surface densities and angular distribution of EROs suggest that the excess originates in high-z galaxy concentrations, possibly young clusters of galaxies. The fainter EROs at K_s>19 mag show some evidence of being more clustered in the immediate 20 arcsec region around the quasars, suggesting an association with the quasars.Comparing with predictions from spectral synthesis models, we find that if the $K_sapprox19$ mag ERO excess is associated with the quasars at $zapprox2$, their magnitudes are typical of >~ L* passively evolving galaxies formed at z~3.5 (Omega_m=0.3, Omega_l=0.7, and H0=70 km/s/Mpc). Another interpretation of our results is that the excess originates in concentrations of galaxies at $zapprox1$ lying along the line of sight to the quasars. If this is the case, the EROs may be tracing massive structures responsible for a magnification bias of the quasars.
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