Blank told reporters this week at the Annual League Meeting in Phoenix, Ariz., that Jones and Jarrett, who are seeking long-term deals, will be "Falcons for life."
"I would give you the same answer for Grady as well as Julio, which I know is a question for our fans and something we definitely want to get done," Blank told the team's official website. "These are two incredible athletes and great players, and great team players, great with other players on the roster.
"Grady's tagging gives the ability to work on that over a longer period of time and I think there will be progress being made on that. With Julio, we're in conversations now not only with him, but his agents now. So, I think there will be progress there. It's always a matter of time, it's give and take, it takes longer than everybody wants, including the franchise, including the players. But we're making good progress I think on both."
Jones agreed to a revised contract before last season in which $2.9 million was moved up. He has two years left on his current contract and is scheduled to earn $9.6 million in 2019 and $11.4 million in 2020.
The star wideout had 113 catches for 1,677 yards and eight touchdowns in 2018. Jones had his sixth 1,000-yard season and was voted to his sixth Pro Bowl.
The Falcons placed the franchise tag on Jarrett on March 4. Atlanta has until the July 15 deadline to work out a long-term contract. If the two sides can't reach an agreement, Jarrett would play the upcoming season under the tag. If he signs the tender, he would earn more than $15 million under the tag.
"We're hopeful; we certainly want to do a long-term deal with him and [keep] him a Falcon," Quinn told the Falcons' official website. "I hope he never graduates. He's a really impactful guy on our team. His leadership and [how] he's emerging in that way is a real factor for us."
Jarrett joined the Falcons as a fifth-round pick in the 2015 NFL Draft out of Clemson. Over his four seasons with the franchise, he has appeared in 61 games (41 starts) and recorded 179 tackles, 14 sacks, three forced fumbles and 40 quarterback hits.