White's agent, Jonathan Feinsod, had no comment when asked if his client is close to agreeing on a new deal.
Atlanta general manager Thomas Dimitroff indicated that he is staying in regular contact with Feinsod, but he offered no immediate timetable.
"We are definitely headed in the right direction in my mind," Dimitroff said. "It's something that has to be contentious. I don't assume that it will be. I don't think the numbers are that far off that we'd consider it to be a long, drawn-out ordeal."
A voice message left for White in Birmingham was not immediately returned. White is working out with former Blazers quarterback Darrell Hackney and former UAB receiver Lance Rhodes.
After catching a career-best 88 passes for 1,382 yards and seven touchdowns, White has missed the first four days of training camp.
"I really can't give you anything of substance to that deal," Falcons coach Mike Smith said Tuesday. "All I can say is the guy you're talking about is one of our best 53 players, and as a coach you want to get all of your best players here. Hopefully he will be here soon."
Under the NFL players association's collective bargaining agreement with the league, White is accruing a fine of $15,888 for each day he skips camp.
The 27-year-old White, the first Atlanta wide receiver with consecutive seasons of 1,200 yards receiving, ranked second in the NFL with 29 third-down catches and led the league 516 yards.
White held out six days as a rookie after the Falcons drafted him 27th overall in 2005 before signing a contract that pays $2.5 million this season. Feinsod will not state the terms he's seeking, but Greg Jennings, a fourth-year receiver with Green Bay, signed a new three-year contract in June worth $27 million.
"We're down a pair of legs with nine wide receivers," Smith said. "They're working extremely hard. We haven't had any pulls and we haven't had anybody miss any snaps, so I think that's very, very positive. We have to make adjustments as far as a coaching staff in preparing our guys for practice."
The Falcons added a 10th receiver Tuesday afternoon when Dicky Lyons of Kentucky signed an undrafted rookie deal.