An almost radial gauge of the electromagnetic potential is constructed for which vanishes arbitrarily fast in timelike directions. This potential is in the class introduced by Dirac with the purpose of forming gauge-invariant quantities in quantum electrodynamics. In the quantum case, the construction of smeared operators is enabled by a natural extension of the free electromagnetic field algebra introduced earlier (represented in a Hilbert space). The space of possible smearing functions K includes vector fields with the asymptotic spacetime behavior typical for scattered currents (the conservation condition in the whole spacetime need not be assumed). This construction is motivated by a possible application to the infrared problem in QED.