The extension to the property was constructed after the 21-month-old from Sheffield went missing in 1991.
The toddler's family believe he was abducted, but police are investigating whether he was accidentally killed.
South Yorkshire Police said it was confident permission for the demolition would be given.
Read more about this and other stories across Sheffield and South Yorkshire
Det Insp Jon Cousins, said he was negotiating with the family who own the farmhouse.
"There is reason for me to consider removing a small part of this farmhouse in order that I can be sure that I have not missed any opportunity to find the answers that I need to," he said.
A photograph from 1991 showed part of the building did not exist when Ben went missing, he added.
A team of 19 South Yorkshire Police officers, forensic specialists and an archaeologist are excavating the farmland where Ben was last seen playing 25 years ago.
They are being assisted by members of the Hellenic Rescue Team and Red Cross.
The search, in its eighth day, was prompted by information given to police following a television appeal in May.
A friend of a digger driver, who had been clearing land with an excavator on the day the toddler went missing, told police the man may have been responsible for Ben's death.
The driver died of cancer in 2015.
On Sunday, the Needham family thanked the volunteers who were working with the police search team.
Police searching for missing toddler Ben Needham on the Greek island of Kos have asked for permission to demolish part of a farmhouse.