A league source told Schefter that Burress is considered among the Patriots' list of emergency replacement possibilities, but the team does not intend to sign the veteran receiver at this time.
Coach Bill Belichick would not confirm the tryout, but indicated that taking a look at a high-profile veteran such as Burress would be business as usual.
"We work out a lot of players. We just try to know who's available out there. We work out and talk to a lot of guys, give them physicals and all that," Belichick said after practice Sunday evening. "I'm not going to comment on any of them individually."
Wes Welker, one of the 10 receivers currently on the roster, echoed Belichick's sentiments.
"I think we work out guys all the time, and so it's nothing new around here. You just kind of roll with it," Welker said. "Whatever Coach Belichick thinks is going to help the team, I'm sure he's going to make those decisions."
Asked whether bringing in Burress, who had 45 catches last season, would be an indictment of the current personnel at receiver, Belichick instead provided a blunt assessment of the whole offense in the team's preseason opener, a 7-6 win Aug. 9 against the Saints.
"I pretty much say the same thing about them as the rest of the offense. When you have 10 punts and two turnovers, we have a long way to go," Belichick said.
Last week, a source told ESPNDallas.com's Calvin Watkins that the Dallas Cowboys were involved in preliminary discussions with Burress' agent, Drew Rosenhaus.
However, Cowboys owner and general manager Jerry Jones later said he hasn't spoken to the agent and was happy with the team's young receivers.
"We haven't even discussed that internally at all," Jones said regarding Burress. "It's not been discussed at any level in our organization one way or the other."
Burress has played for three NFL teams in a 10-year career, collecting 550 catches for 8,457 yards and 63 touchdowns.
In September 2009, Burress was sentenced to two years in prison for violating gun laws in New York after accidentally shooting himself in the leg while at a Manhattan nightclub. He pleaded guilty to a lesser firearms charge.
Burress was released three months early for good behavior, and signed with the Jets last season. He tied for the team lead with eight touchdown receptions and finished with 612 yards and 45 receptions.
Mike Rodak is a contributor to ESPNBoston.com. Information from ESPNDallas.com's Calvin Watkins was used in this report.