Manziel, 24, didn't play in the NFL at all last season after he was cut by the Cleveland Browns in March 2016.
Burkhardt fired Manziel in Feb. 2016 after the quarterback's ex-girlfriend, Colleen Crowley, made domestic violence allegations against Manziel. The former Texas A&M star then hired Drew Rosenhaus to be his agent, only to have Rosenhaus fire him in April 2016.
The news of a potential comeback comes just a day after Manziel told Judge Roberto Canas that he was cautious of working with the NFL due to how the league has handled player issues in the past, per Naheed Rajwani of the Dallas Morning News.
Manziel was in court to discuss the negotiated agreement between his legal team and the Dallas County district attorney's office to dismiss the misdemeanor assault charges he faces from the alleged incident with Crowley.
Judge Canas was concerned that Manziel missed a deadline in fulfilling the terms of his conditional agreement, which requires him to take an "anger management course, attend a domestic violence victim impact panel, and participate in either the NFL's substance abuse program or go to a court-approved drug and alcohol rehab facility," per Rajwani.
"Everything has been going extremely smoothly and my life is trending upward, so I don't even want to let this get anywhere near the rabbit hole that you were describing," Manziel told the judge. "This situation is in my hands... I need to get my life in order. These are the things I need to do."
Even if a team gives Manziel a shot and he returns to the NFL, he could still be facing up to a six-game suspension under the league's domestic violence policy.
In 14 career games with the Browns over two seasons, Manziel—the 22nd overall pick in the 2014 NFL draft—threw for 1,675 yards, seven touchdowns and seven interceptions, completing 57 percent of his passes. He also rushed for 259 yards and an additional score, though his brief career with the Browns was marked as much by off-field incidents and concerns as it was for his play on the field.