By measuring the critical current versus the applied magnetic field I-c(Phi) of an Al superconducting loop enclosing a soft Permalloy magnetic dot, we demonstrate that it is feasible to design a linear magnetic flux amplifier for applications in superconducting quantum interference devices. The selected dimensions of a single-domain Permalloy dot provide that the preferential orientation of the magnetization is rotated from the perpendicular direction. By increasing an applied magnetic field, the magnetization of the dot coherently rotates toward the out-of-plane direction, thus providing a flux gain and an enhancement of the sensitivity. As a result of a pronounced shape anisotropy, the flux gain generated by the dot can be tuned by adjusting the dimensions of the dot. (C) 2005 American Institute of Physics.