The caravans and associated vehicles are said to have relocated to a private access road next to the football ground on Friday night (June 8).
Eye witnesses say the caravans then moved just a few feet onto the Chester FC car park after bailiffs arrived to evict them.
Staff from local businesses told The Chronicle they are unhappy with the behaviour of the children.
They claim problems on their site have included going in and out of a warehouse where large articulated lorries are operating, scavenging from a skip and leaving a mess and using a rear area as a public toilet. The site is traditionally popular with travellers over the summer.
Police are investigating damage to a car parked nearby after scratches were made on the bonnet of the vehicle.
A Cheshire Police spokesman said: “Police were called at 11.13am on Monday 11th May to Sovereign Way, Chester, after reports of criminal damage to cars. Anyone with information is asked to call Cheshire Police on 101 quoting incident number 90398.”
Police appear to be carrying out routine patrols at the site.
The Chronicle has approached Cheshire West and Chester Council for a comment as owners of the football ground. Cheshire and Warrington Traveller Team will be visiting the site. More information is expected to be provided following the visit.