The mechanism of superconductivity and magnetism and their possible interplay have recently been under debate in pnictides. A likely pairing mechanism includes an important role of spin fluctuations and can be expressed in terms of the magnetic susceptibility χ. The latter is therefore a key quantity in the determination of both the magnetic properties of the system in the normal state and of the contribution of spin fluctuations to the pairing potential. A basic ingredient to obtain χ is the independent-electron susceptibility χ₀. Using LaO_1−xF_xFeAs as a prototype material, in this report we present a detailed ab initio study of χ₀(q,ω) as a function of doping and of the internal atomic positions. The resulting static χ₀(q,0) is consistent with both the observed M-point-related magnetic stripe phase in the parent compound and with the existence of incommensurate magnetic structures predicted by ab initio calculations upon doping.