The Houston Texans selected Davenport in the fourth round (130th overall) of the 2017 NFL draft.[3] On May 12, 2017, the Texans signed Davenport to a four-year, $2.98 million contract that included a signing bonus of $586,415.[4] He played in 11 games with four starts as a rookie.
On August 31, 2019, Davenport, Johnson Bademosi, 2020 and 2021 first round picks, and a 2021 second-round pick were traded to the Miami Dolphins in exchange for Laremy Tunsil, his teammate Kenny Stills, a 2020 fourth-round pick and 2021 sixth round pick.[6] On September 12, 2019, Davenport suffered a hyperextended knee and a cracked fibula during practice and was placed on injured reserve the following day.[7] He was designated for return from injured reserve on October 31, 2019, and began practicing with the team again.[8] He was activated off injured reserve on November 16, 2019.[9]
On April 25, 2022, Davenport signed with the Chicago Bears.[11] He was released on August 23, 2022.[12]
Arizona Cardinals
On November 16, 2022, Davenport was signed to the practice squad of the Arizona Cardinals.[13] He signed a reserve/future contract on January 11, 2023.[14] He was released on June 14.[15]
New York Giants
On August 15, 2023, Davenport signed with the New York Giants following a workout.[16] He was released on August 27.[17]
On July 23, 2024, Davenport signed with the Atlanta Falcons.[20] He was released on August 27, and re-signed to the practice squad.[21][22] He was released on September 3.