GRB 100205A is a Gamma Ray Burst (GRB) which is suspected to be at $11{leq}Z{leq}13.5$ due to its very red H-K color ($(H-K)_{vega}=2.1{pm}0.5$). We observed a field centered at GRB 100205A with the Wide Field Camera (WFCAM) at the United Kingdom Infrared Telescope (UKIRT) in Hawaii, so as to find a 11 < z < 13 quasar that could be located around the GRB. The images were obtained in J, H, and K filters covering a square area of 0.75 $deg^2$ to the depths of 22.5, 21.4, and 20.2 in Vega magnitude at $5{sigma}$, respectively. Also using a z-band image observed by MegaCam in Canada France Hawaii Telescope (CFHT), we found 12 candidates that have colors consistent with a quasar at 11 < z < 13 with two criteria; (1) non-detection in z-, J-bands and $(H-K)_{vega}$ > 1.6 (2) only detection in K-band with $(Hlimit-K)_{vega}$ > 1.6. However, we also find 627 red ($(H-K)_{vega}$ > 1.4) objects that are likely to be old or dusty galaxies at $z{leq}3$, so the 12 candidates could be these red objects. These red objects are found to be strongly clustered in the Ultra Deep Survey (UDS) fields of UKIRT Infrared Deep Sky Survey (UKIDSS) than those in the GRB 100205A field. We suggest a lack of a strongly clustered region surrounding an extremely high-redshift GRB with some limitations.