The mother-of-three is alleged to have waded into an argument that arose after cage fighter Reid parked in a disabled bay at a shopping centre near their Sussex home.
Price has a disabled son, Harvey, from her relationship with former soccer star Dwight Yorke.
Reid, who won Celebrity Big Brother, was confronted by a woman and her partner who objected to him using the space.
Sussex Police were called to the ensuing disturbance, but said the fight was verbal rather than physical.
A force spokesman said: “Sussex Police attended the Goldstone Retail Park in Hove at around 1.30pm on Good Friday afternoon following reports of an argument between two men.
“It would appear that a dispute had arisen over the occupation of a disabled parking bay and also involved the partner of one of the men and the wife of the other.”
All four were questioned by police at the scene, the former site of Brighton and Hove Albion FC’s football ground.
No arrests have yet been made, nor any charges brought, and inquiries are continuing.
Police said it was not known if any of Price’s children were present during the row, or if the couple who challenged the use of the parking space were themselves disabled.
The retail park houses stores including JJB Sports, Toys R Us, Burger King and Comet.