Garland police said Tuesday they believe Talib and his mother, Okolo Talib, shot at the man March 21. The man wasn't injured. Earlier that day, the man had been listed as a suspect in a disturbance and was charged with assault and interference with an emergency phone call from that incident.
Authorities issued arrest warrants for aggravated assault with a deadly weapon for Talib and his mother. She turned herself in Tuesday.
Police say Aqib Talib is set to turn himself in later this week. His agent, Todd France, did not immediately return a call.
Aqib Talib's bail will be set at $25,000, according to the Garland Police Department.
"We are deeply troubled by the serious charges filed against Aqib Talib," Bucs general manager Mark Dominik said in a team statement. "Due to current labor circumstances, we will withhold any further comment or action."
A Garland police spokesman said in a radio interview with Tampa station WDAE (620 AM) Tuesday afternoon that detectives met with Aqib Talib last week and continued their investigation before making the decision to charge him with a crime. The spokesman said the charge is a second-degree felony, which can carry a prison sentence of five to 20 years.
Okolo Talib was booked Tuesday morning on a charge of aggravated assault with a deadly weapon with an additional charge of felon in possession of a firearm, which was added based on a prior conviction. Her bond was set at $25,000 for the assault charge and $5,000 for the possession of a firearm charge.
Aqib Talib, who went to L.V. Berkner High School in the Dallas suburb of Richardson, played at the University of Kansas and was a first-round pick by the Buccaneers in 2008. He's also been in trouble before. He was suspended by the NFL for the first game of last season after a 2009 altercation with a cab driver.
He was entered into a pretrial diversion program and ordered to attend anger management classes after the incident with the cab driver, which whom he reached a financial settlement.
Although NFL players are currently locked out, commissioner Roger Goodell said last week they still are subject to the league's personal conduct policy and disciplinary action can be taken after the labor situation is resolved.
The 25-year-old Talib has 15 interceptions in three NFL seasons.
Pat Yasinskas covers the NFC South for ESPN.com. Information from The Associated Press contributed to this report.