The Florida Times-Union first reported that the sides were close to agreeing on a contract.
The 25-year-old Jones took over as the starter for the final nine games of 2016 after Roy Miller suffered a torn Achilles. Jones finished the season with 32 tackles (four for loss) and one batted pass.
Jones signed as an undrafted rookie free agent in April 2013 and played in eight games that season. The following year he appeared in all 16 of the Jaguars' games, making two starts, and finished with 39 tackles, three sacks and a forced fumble.
In 2015, he recorded 16 tackles, two sacks and a forced fumble in 15 games.
Jones' play last season showed that he can handle the starting job and might make the 30-year-old Miller expendable. Even if the Jaguars keep Miller -- who is due a $400,000 roster bonus on March 13 and is scheduled to make $3.64 million in 2017 -- and he continues to play as well as he did before he was hurt, Jones has shown he can handle a bigger load.
Miller has been the starting nose tackle for four seasons and played well, but he turned 30 in July and has had knee issues that required surgery following the 2014 season to repair meniscus damage.