We're not sure if this could be considered normal.

Most swans, regardless of species are not going to let another animal get close without reacting. Now having said this, if the Black Swan is someone's captive swan and was raised around a dog, then this could possibly explain the swan's behavior. Another possibility is that the bird is very young and has no idea how to protect itself or even recognize a possible predator and the ultimate threat. In any case, this behavior can get the swan seriously injured or killed. For this reason, we would strongly suggest that you try to capture the bird (safely without harming you or the bird or contact a wildlife rescuer) and try to find its owner. If the swan can be identified through a band or microchip, you may be able to return it to its owner. If there is no identification, you can either find it a safer home, or keep it but keep it indoors at night and safe from nocturnal predation. However, this also means that you also will need to keep a close eye on it during the day. The Regal Swan