You can use PROC REG, and that is in fact what is done in the note I referred to. But as described there, proper evaluation of collinearity in a logistic model requires a weighted analysis in PROC REG. I encourage you to carefully and fully read through the collinearity section. PROC GENMOD is used to produce the necessary weights for a variety of model types. In the case of a logistic model, the necessary weights are just p*(1-p), so they could be produced from saving the predicted probabilities from the fitted model followed by a DATA step to compute these weights.
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