Texas began selling beer at other athletic events at the urging of athletic director Steve Patterson in 2014, but not at football games.
Fenves took over the job Wednesday. In his first news conference, Fenves said school officials have studied beer sales and found no security problems at other events.
The plan would still need approval by University of Texas System Chancellor William McRaven, and would likely be voted on by the board of regents. McRaven's predecessor, Francisco Cigarroa, had opposed beer sales.
Personally, Fenves said he rarely drinks beer, but wants Longhorns fans to be able to have it at the games.