https://nypost.com/2003/07/02/big-east-leans-on-hoops/

Nice historical article that was posted on the other site. Xavier was being floated as the other potential non-football addition (along with Marquette) in 2003 for the Big East. This would have made the additions as Cincinnati, Louisville and South Florida as full-members, and then Marquette and Xavier (not DePaul) as the non-football members. The rumor for Xavier not being selected at the time was that Tranghese did not want to poach from more than one conference. Getting the Crosstown Shootout in the Big East would have been epic.

This would have meant that DePaul would have stayed in Conference USA through 2005, and then likely moved to the A-10 (along with SLU) for 05-06. For the 2013 realignment cycle, DePaul would have been likely considered for the NBE - although depending on how their time in the A-10 goes, may not even have been taken. I believe the market draw of Chicago would have pushed them in regardless.