We investigate the relation between the radio (Fr) and optical (Fo) flux densities of a variety of classes of radio transients and variables, with the aim of analysing whether this information can be used, in the future, to classify such events. Using flux density values between 1 and 10 GHz and the optical bands V and R, we build a sample with a total of 12 441 Fr and Fo measurements. The sample contains both Galactic objects, such as stellar sources and X-ray binaries, and extragalactic objects, such as gamma-ray bursts and quasars. By directly comparing the two parameters, it is already possible to distinguish between the Galactic and extragalactic populations. Although individual classes are harder to separate from the Fr - Fo parameter space to a high accuracy, and can only provide approximations, the basic approach provides an already useful foundation to develop a more accurate classification technique. In addition, we illustrate how example objects from different classes move in the parameter space as they evolve over time, offering a feature that could be used to reduce the confusion between classes. A small, blind test of the classification performance is also undertaken using a catalogue of VLA FIRST transient and variable sources, to demonstrate the advantages and current limitations of the approach. With more multiwavelength data becoming available in the future, we discuss other classification techniques which the Fr - Fo method could be combined with and potentially become an important part of an automatic radio transient classification system.