Jones is fresh off a season in which he caught 104 passes for 1,593 yards and six touchdowns for Atlanta.
Terms of the deal are expected to include $47 million in guaranteed money.
Blank said that the team is currently in contract discussions with Jones' camp.
“We are in the middle of those discussions,” Blank said on Sunday. “We expect Julio to be lifer for the Falcons. We are moving forward and have every reason to be positive and be enthusiastic about it.”
Jones caught 104 passes for 1,593 yards and six touchdowns last season.
The team and Jones are both interested in negotiating a contract extension before Jones becomes a free agent. While the two sides haven't begun talking yet, ESPN reported that there is a "general sense around the team" that the deal will be done before training camp.
Falcons traning camp opens July 31.
“I’m not going to hold out for anything," Jones said. "My teammates need me. I’m being selfish if I’m not here and doing what I need to do.”
If no deal is reached, Jones can become an unrestricted free agent after the 2015 season. Jones produced 1,593 receiving yards and six touchdowns on 104 catches last season, which earned him a Pro Bowl selection.
Jones can become an unrestricted free agent after this season, yet no talks on a new deal have been discussed despite the expressed desire from front office personnel to keep him on the team. General manager Thomas Dimitroff traded away five picks in the 2011 draft in order to select him.
The 26-year-old Jones has been worth the gamble. He landed a Pro Bowl spot last season, setting the franchise record with 1,593 receiving yards on a whopping 104 catches while coming back from a fractured foot sustained the previous year.
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