West Midlands Police said they were called on Sunday to an address in Solihull, near Birmingham, where the two parked cars suffered minor damage.
The force said the driver had left his details with a member of the public before leaving on foot.
Images surfaced online of a damaged white Range Rover as well as a picture that appeared to show the Villa midfielder in slippers and a bright blue hoodie.
Less than 24 hours before the incident, the 24-year-old Villa captain launched a video appeal for people to stay at home during the government-enforced lockdown.
In the video, he said: "To help save lives you must stay at home.
"Only leave your house to buy food, buy medicine or to exercise and always remember to stay at least two metres apart.
"This is urgent, protect the NHS, stay home, save lives."
In a statement about the incident, the West Midlands force said: "Officers are investigating the circumstances and anyone with information has been asked to get in touch."