Upon trying to work with Lewian's answer above, I found it to be lacking in clarity, so I've attempted to use his answer to write my own version below.
A linkage is a measure of closeness between pairs of clusters. It depends on the distance between the observations in the clusters.
Let's assume that an outlier is defined as an object that is "far" from all the others.
In the case of a complete linkage, we are using the largest value of the distance function over the observations of the two clusters. Therefore, if the other cluster is large (with observations spread), then there might be some observations that are much closer than the observations used for the maximum distance calculation; however, they would not be taken into account when using the complete linkage. Therefore, the singleton would not necessarily be an outlier.
In the case of a single linkage, we are using the smallest value of the distance function over the observations of the two clusters. Therefore, a singleton's minimum distance to all clusters is comparatively (to the complete linkage) large, so its distance to all other observations is comparatively (to the complete linkage) large. Therefore, if even by using the smallest value we find that some observations are classified as singletons, then chances are that they actually are indeed outliers.
The average linkage and the centroid linkage seem to be between the two extremes of the complete linkage and the single linkage. Therefore, I would say that the single linkage is most suitable for detecting outliers.