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Here, we study the small-x evolution equation for the gluon generalized parton distribution Eg of the nucleon. It is shown that Eg at vanishing skewness exhibits the Regge behavior identical to the Balitsky-Fadin Kuraev-Lipatov pomeron despite its association with nucleon helicity-flip processes. We also consider the effect of gluon saturation and demonstrate that Eg gets saturated in the same way as its helicity-nonflip counterpart Hg. Our result has a direct impact on the modeling of Eg as well as the small-x contribution to nucleon spin sum rules