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We report a detailed investigation of GdO$_{1-x}$F$_{x}$FeAs (x = 0, 0.07 and 0.14) samples by means of high-field/high-frequency electron spin resonance (HF-ESR) together with measurements of thermodynamic and transport properties. The parent GdOFeAs compound exhibits Fe long-range magnetic order below 128 K, whereas both doped samples do not show such order and are superconducting with T$_c$ = 20 K (x = 0.07) and T$_c$ = 45 K (x = 0.14). The Gd$^{3+}$ HF-ESR reveals an appreciable exchange coupling between Gd and Fe moments, through which the static magnetic order is clearly seen in the parent compound. Owing to this coupling, HF-ESR can probe sensitively the evolution of the magnetism in the FeAs planes upon F doping. It is found that in both superconducting samples, where the Fe long-range order is absent, there are short-range, static on the ESR time scale magnetic correlations between Fe spins. Their occurrence on a large doping scale may be indicative of the ground states' coexistence.