Dimitroff's stated goal is locking up Freeman before veterans arrive for training camp Thursday.
"I've always said that I think it's going to be a fairly expeditious negotiation, but you never know," Dimitroff said. "I'd love it to happen."
Freeman, scheduled to earn $1.8 million in 2017, which is the final year of his rookie contract, was reportedly offered a five-year contract worth between $7 million and $8 million per season. Among running backs, only franchise-tagged Le'Veon Bell of the Pittsburgh Steelers ($12.2 million) is scheduled to make more than $8 million in 2017.
Dimitroff also confirmed rookie pass rusher Takkarist McKinley will be limited to start training camp. McKinley had surgery to repair a torn labrum in March, and his expected recovery time was four to six months.
Freeman's agent said during Super Bowl Media Night that Freeman should be paid "like the elite back he is."
The 25-year-old Freeman started all 16 regular-season games in 2016, leading the Falcons with 1,079 rushing yards to go with 462 receiving yards on 54 receptions. Freeman had 13 total touchdowns.
Freeman has 3,175 yards from scrimmage the past two seasons.