Burress traveled to Pittsburgh on Monday and will visit with the team Tuesday, according to the source.
Burress played last season with the New York Jets after spending nearly two years in prison for illegal possession of a firearm.
Despite missing the 2009 and 2010 seasons, Burress was productive with the Jets, hauling in 45 receptions and eight touchdowns. But the 35-year-old has remained unsigned throughout this season despite reportedly drawing interest from multiple teams.
The 6-foot-5 Burress would significantly bolster an injury-plagued receiving corps in Pittsburgh (6-4, second in the AFC North). Starting wideout Antonio Brown has missed the past two games due to a sprained ankle, and Jerricho Cotchery also was injured late in Sunday's loss to the Baltimore Ravens.
The eighth overall selection in the 2000 NFL draft, Burress spent his first five seasons with the Steelers before signing as a free agent with the New York Giants in 2005.
ESPN NFL Insider Adam Schefter contributed to this report.