This paper describes an attention-target approach detection technique for a vehicle reminder system. For a moving vehicle with some function to avoid traffic accidents, it is important to detect if the attention-target is approaching or not. Assuming an attention-target carrying a beaconing device to broadcast its existence, this paper discusses the performance of the approaching detection achieved only by using the received signal strength indicator (RSSI) of the repeatedly radiated beacons from the target. The detection reliability under multipath environment is theoretically analyzed and compared with the results obtained by a simulation technique. It is revealed that the slope of the variation in the RSSI can be used to detect the target approach since the successive RSSI samples can be well-approximated to a linear function of the receiving time. It is also revealed that the beaconing frequency is a crucial element for characterizing the detection error rate, and accepting some detection delay leads to the reduction of detection error rate, which can be further improved by applying multiple antenna diversity technique.