Six caravans and several other vehicles are parked on private land at the site on South Pier Road.
The Cheshire and Warrington Traveller Team visited the museum today (January 23) and have spoken to staff there.
According to a spokesperson from Cheshire West and Chester Council a manager has appointed bailiffs to have them moved.
On January 18 travellers were camping on council land at Wellington Road car park in Ellesmere Port.
The Cheshire and Warrington Traveller Team carried out welfare assessments on the group.
Notice was served, giving them 24 hours to vacate the land.