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.
Beasley, the eighth overall pick in this year's draft, racked up 33 sacks during his time at Clemson, earning him the reputation as a big-time pass threat, but he wants to show the Atlanta coaching staff that he can play in all situations.
"I think I'm an every-down player. I think that's just motivation for me to go out there and prove that I can be an every-down player," he said.
Beasley will get a chance to live up to that statement, as the Falcons plan to throw the rookie into the fire to help a shaky linebacker corps.
Holmes missed 12 games last season with a foot injury. He is listed as out indefinitely.