The BBC said 31-year-old Rooney was stopped by police near his home in Cheshire, northwest England, on Thursday night.
Rooney was seen posing in a selfie with cricketer Jack McIver in a bar in Alderley Edge earlier that day.
McIver shared the photo of the pair in the Bubble Room on Instagram at around 10:00pm (2100 GMT) that day with the comment: “International Break #legend”.
Rooney, England’s all-time record goal-scorer, announced his retirement from international football last week, having scored 53 goals in 119 appearances for his country.
He made his decision despite England manager Gareth Southgate offering to recall him for the World Cup qualifier against Malta on Friday.
Rooney re-joined boyhood club Everton in the pre-season from Premier League rivals Manchester United.
Rooney scored in his first two Premier League games of the 2017/18 campaign, with the forward on target last month in a 1-0 win over Stoke City and again in a 1-1 draw with Manchester City.