Context. The two nuclei of the starburst galaxy Arp220 contain multiple compact radio sources previously identified as radio supernovae or supernova remnants. Aims. In order to search for an embedded radio AGN, or other possible exotic objects, we have carried out a program of VLBI monitoring at 6 cm over three epochs each separated by four months. Methods. Combining the new data with existing data at 6 cm and 18 cm (spanning 4 and 12 years respectively) we are able to characterise source flux density variability on a range of time-scales. Additionally we analyse the variability of sources in shape and position. Results. We detect rapid (< 4 months) variability in three sources (W7, W26 and W29). These sources show possible superluminal motion (> 4c) of jet-like features near rapidly varying almost stationary components. These enigmatic sources might be associated with an AGN or a highly beamed microquasar (i.e. microblazar). Other hypotheses include that the apparent variability is intrinsic and is produced by neutron star powered central components within a supernova remnant, by a sequence of several supernovae within super star clusters, or is extrinsic and is produced by Galactic interstellar scintillation of very compact non-varying objects. Conclusions. A microquasar/microblazar origin seems to be the best explanation for the nature of the variable sources in Arp220.