This topic comes up all the time by Memphis fans and ONLY Memphis fans. They are not elite. Elite is winning multiple national championships over your history and consistent tourney success over generations and/or with different coaches. They do not qualify. The elite (arguably) are Duke, UNC, UK, Indiana, UCONN, Syracuse, UCLA, Arizona, Kansas, Michigan State.
Memphis is however, IMO in the second tier of schools which have a nice history (often with one coach) or a recent (last 10 years or so) run of success which places them in the next tier. Memphis has had success with 2 coaches, but really only Cal took them to the brink of elite, right before he left them standing at the alter. Pastner has not taken them over the threshold, in fact he has lost some momentum (on the court - not recruiting). The other teams (arguably) in the next tier are Villanova, Pitt, Butler, Louisville (although as long a Ricky P is there they could be in the above list), Ohio State, maybe Michigan (with Bielein and their history), Florida (they should be above, but their fanbase is sooo weak), Georegtown, and Gonzaga.
Then of course there are teams with periods of great success, but an inability to maintain it over the long-haul and/or recently. Tennessee, Texas, Purdue, NC State, Maryland, Arkansas, Wisconsin (could argue above, but playing style limits overall perception of program), Kansas State.
Just my thoughts though