Smartphone apps for exposure notification and contact tracing have been shown to be effective in controlling the COVID-19 pandemic. However, Bluetooth Low Energy tokens similar to those broadcast by existing apps can still be picked up far away from the transmitting device. In this paper, we present a new class of methods for detecting whether or not two Wi-Fi-enabled devices are in immediate physical proximity, i.e. 2 or fewer meters apart, as established by the U.S. Centers for Disease Control and Prevention (CDC). Our goal is to enhance the accuracy of smartphone-based exposure notification and contact tracing systems. We present a set of binary machine learning classifiers that take as input pairs of Wi-Fi RSSI fingerprints. We empirically verify that a single classifier cannot generalize well to a range of different environments with vastly different numbers of detectable Wi-Fi Access Points (APs). However, specialized classifiers, tailored to situations where the number of detectable APs falls within a certain range, are able to detect immediate physical proximity significantly more accurately. As such, we design three classifiers for situations with low, medium, and high numbers of detectable APs. These classifiers distinguish between pairs of RSSI fingerprints recorded 2 or fewer meters apart and pairs recorded further apart but still in Bluetooth range. We characterize their balanced accuracy for this task to be between 66.8% and 77.8%.