On December 5, 2016, it was announced that Saubert had accepted an invitation to play in the 2017 East–West Shrine Game. He impressed scouts and analysts throughout practices for the Shrine Game, displaying his athleticism, receiving ability, and received praises from multiple media members, including NFL analyst Mike Mayock. On January 21, 2017, Saubert played in the East–West Shrine Game and was part of an East team that lost 10–3 to the West. Unfortunately, he was unable to record a reception although he was targeted twice. On January 26, 2017, it was announced that Saubert would be a late addition to play in the 2017 Senior Bowl. He Attended two days later and was a part of Cleveland Browns' head coach Hue Jackson's South team that defeated the North 16–15. He was unable to record a reception with top draft prospects O. J. Howard, David Njoku, and Gerald Everett on his team and only having a day of practice. Saubert was one of 19 collegiate tight ends to receive an invitation to the NFL Scouting Combine in Indianapolis, Indiana. He tied for second amongst his position group in the bench press, fifth in the broad jump, and eighth in the vertical jump and opted to only perform those drills. On March 28, 2017, Saubert attended Iowa State's pro day and performed all of the combine drills and positional drills. He ran receiving drills with Cincinnati Bengals'tight ends coachJonathan Hayes for the 33 team representatives and scouts who attended from 22 NFL teams. At the conclusion of the pre-draft process, Saubert was projected to be a fifth or sixth round pick by NFL draft experts and scouts. He was ranked the 12th best tight end prospect in the draft by CBS Sports and was ranked the 13th best tight end by NFLDraftScout.com.
Atlanta Falcons
The Atlanta Falcons selected Saubert in the fifth round of the 2017 NFL Draft. He was the first player selected from Drake since Pat Dunsmore was selected in the fourth round of the 1983 NFL Draft. Saubert was the 20th player drafted in Drake University history and the 12th tight end drafted in 2017. On May 11, 2017, the Atlanta Falcons signed Saubert to a four-year, $2.62 million contract that includes a signing bonus of $227,388. With the departure of Jacob Tamme in free agency, Saubert competed for the starting tight end job throughout training camp, against Austin Hooper and Levine Toilolo. Head coach Dan Quinn named him the third string tight end to begin the regular season. He made his professional regular season debut in the Atlanta Falcons' season-opening 23–17 victory at the Chicago Bears. He played in 14 games his rookie year but did not record any statistics. Saubert had five catches for 48 yards in 2018 as he saw action in all 16 games, including one start.
On August 12, 2019, Saubert was traded to the New England Patriots for a conditional seventh-round draft pick in the 2020 NFL Draft. He was released during final roster cuts on August 31, 2019.
On November 30, 2019, Saubert was signed by the Chicago Bears off the Raiders practice squad. He caught two passes for 21 yards during the 2019 season. Saubert was placed on the reserve/COVID-19 list by the Bears on July 29, 2020.
Personal life
Saubert is a second cousin of former New York Giants guard Rich Seubert. The two have different last names because of a family disagreement.
