Arsenal defender Andre Santos was arrested after it was claimed the Brazilian had driven his car at speeds of up to 130mph (209kph) in a bid to escape from police, British media have reported.
He was eventually stopped by police close to Arsenal's training ground at London Colney on Friday.
A police spokesman said: "Shortly after 9.30am on Friday 17 August, a 29-year-old man was arrested on suspicion of dangerous driving and failing to stop for police on the A1.
"Officers' attention was drawn to the vehicle due to the manner of its driving. The man has been bailed to return at a date in mid-September to a North London police station."
The man was not breathalysed, police added. He could be jailed for up to two years if convicted of dangerous driving.
Santos was on the bench for Saturday's match against Sunderland but did not play in the 0-0 draw.