Joseph, 28, is a former second-round pick of the Giants back in 2010. He spent four seasons in New York before departing in 2014 for a five-year, $31.5 million contract with the Vikings.
Joseph has two years remaining on his current deal and stands to make base salaries of $6.15 million and $5.15 million in the next two years.
In 2016, Joseph appeared in all 16 games and recorded 77 tackles, four sacks, and three forced fumbles. Pro Football Focus has him rated as the No. 14 interior defender out of 125 qualifying players.
Barr, 25, was taken with the No. 9 overall pick by the Vikings back in 2014. He was in the final year of his four-year $12,743,500 rookie contract and set to make a base salary of $2,157,750 for the 2017 season when the Vikings picked up his fifth-year option a few months ago.
The fifth-year option will run the Vikings around $12.306 million for the 2018 season but is guaranteed only for injury and won’t prevent them from working on a long-term extension over the next year.
In 2017, Barr appeared in all 16 games and recorded 71 tackles, two sacks, a fumble recovery, a forced fumble and four pass defenses. Pro Football Focus has him rated as the No. 79 linebacker out of 87 qualifying players.