The company, which spends £5 million on advertising, is conducting its search via the intermediary Oystercatchers.
Center Parcs is in talks with eight agencies, thought to include several ad shops.
The holiday company has previously worked with Beattie McGuinness Bungay, after the agency won a pitch to handle the business in 2010.
BMB went on to create TV work showing families taking part in outdoor activities.
One television spot, which featured on-screen copy that read "4 night breaks from £249 for 4 people", was banned by the Advertising Standards Authority after a viewer argued that it was not clear that the break had to be taken in January.
McCann Erickson Manchester held the Center Parcs account before BMB, creating a 2007 campaign called "feeling free".