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.
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