The house, made for BBC Two series Toy Stories, which May hosts, will be knocked down on Tuesday if a new owner cannot be found.
Dismantling and reassembling the house will cost about ВЈ50,000, according to the BBC.
Top Gear, where May also works, has launched a campaign to save the house from demolition.
Legoland says it is too expensive to move the house, constructed at Denbies Wine Estate in Dorking, Surrey, by 1,000 volunteers.
Building falls on high-reach excavator during demolition - VIDEOWhite House outlines fuel plan
