Vinny Testaverde (1986), Gino Torretta (1991), and Ken Dorsey (2001) have all won the award in the past.
Morris is coming off a tremendous junior season in which he threw for 3,345 yards and 21 touchdowns. He had one of the most prolific seasons of any quarterback in school history.
Johnson was a five-star recruit from a local high school, and made a big impact in his first year. He broke Clinton Portis' freshman rushing record with 947 yards.
Semifinalists for the Maxwell Award will be announced Oct. 29, while the three finalists will be unveiled Nov. 18. The 2013 Maxwell Award winner will be announced Dec. 12 as part of the Home Depot ESPNU College Football Awards Show.