To solve this question, let's work backwards.
We are given that the day before the day before yesterday is three days after Saturday.
Let's assume today is X.
So, the day before yesterday will be X-2, and the day before the day before yesterday will be (X-2)-1, which can be simplified to X-3.
According to the given information, X-3 is three days after Saturday.
Since Saturday is two days before X-3, we can determine that X-3 is actually a Tuesday.
Therefore, the day before yesterday (X-2) is a Monday, and today (X) is a Tuesday.
Hence, the correct answer is E) Friday.