Williams passed for 1,912 yards and 21 touchdowns with just four interceptions after replacing Spencer Rattler as the Sooners' starter this season. Rattler transferred last month to South Carolina.
Williams, a true freshman this past season, said in his tweet that he went to Oklahoma with a game plan, "but with all of the recent changes, I need to figure out what is the right path for me moving forward."
Williams said that staying at Oklahoma would "definitely be an option" as he goes through the process. He explained that, as a student-athlete, the only way under NCAA rules he could speak to other schools and "see who may offer the best preparation and development for my future career is by entering the portal."
After Lincoln Riley left abruptly to take the Southern California coaching job at the end of November, the Sooners replaced him last month with Brent Venables, the former Clemson defensive coordinator. Venables brought in Jeff Lebby from Ole Miss to be the Sooners' offensive coordinator.
Venables and Oklahoma athletic director Joe Castiglione released a joint statement Monday that read in part: "While we believe OU provides Caleb the best opportunity to develop as a player and realize his goals for college and beyond, we respect his right to explore his options following key staffing changes here."
The statement also mentions Lebby and refers to him as "one of the most elite offensive coordinators and quarterback developers in the country." Lebby played a key role in Ole Miss quarterback Matt Corral's development.
In what could be Williams' finale with Oklahoma, the quarterback threw for three touchdowns with interim coach Bob Stoops patrolling the sideline last week as the Sooners raced past Oregon 47-32 in the Alamo Bowl, capping an 11-2, yet topsy-turvy, season.