Understanding and monitoring the solar corona and solar wind is important for many applications like telecommunications or geomagnetic studies. Coronal electron density models have been derived by various techniques over the last 45 years, principally by analysing the effect of the corona on spacecraft tracking. Here we show that recent observational data from very long baseline interferometry (VLBI), a radio technique crucial for astrophysics and geodesy, could be used to develop electron density models of the Sun's corona. The VLBI results agree well with previous models from spacecraft measurements. They also show that the simple spherical electron density model is violated by regional density variations and that on average the electron density in active regions is about three times that of low-density regions. Unlike spacecraft tracking, a VLBI campaign would be possible on a regular basis and would provide highly resolved spatial-temporal samplings over a complete solar cycle.