New York placed the original-round restricted tender on Qvale, which will cost them $1.907 for the 2018 season.
Qvale, 27, signed on with the Jets as an undrafted free agent out of Nebraska back in 2014. He just finished a three-year, $1,575,000 contract.
In 2017, Qvale appeared in all 16 games for the Jets and was rated by Pro Football Focus as the No. 58 overall tackle out of 81 players.
Dozier, 26, is a former fourth-round pick of the Jets back in 2014. He played out the final year of his four-year, $2,520,584 contract with the Jets and was testing the open market for the first time in his NFL career.
In 2017, Dozier appeared in 14 games for the Jets and played a total of 248 snaps for the Jets, according to Pro Football Focus.