Design space exploration (DSE) is a key activity in any embedded system design flow. With the remarkable increasing in the connectivity to the internet, embedded systems are becoming the target of different cyber-attacks. As security emerges as a major design concern, DSE should be aware of the security aspect at a higher level of abstraction. On the other hand and to our best knowledge, there is no a comprehensive survey on this topic, hence the need to establish a comprehensive survey for existing security-aware DSE approaches for embedded systems at the system level. To meet this objective, we first selected and summarized twenty-two pertinent works. They were analyzed based on a set of criteria. The outcomes of this survey are a set of recommendations that can help embedded systems designers to better dealing with security at system-level DSE stage. The presented survey ends by proposing some potential promising future trends that can be investigated by researchers to pursue the research in related topics.