On Wednesday, MPI said it believed the disease was present on a farm in the Oamaru area which had had ''a direct connection'' with one of two other affected farms, both in Waimate.
The owner of those affected farms, Aad Van Leeuwen, later told the ODT he had sold bobby calves to the Otago farmer.
The Otago Daily Times understands the Otago farm is in the Maheno area.
An MPI spokeswoman yesterday said it was ''bound by the Privacy Act'' and legally could not identify the farm.
Asked how it had been able to identify the two Van Leeuwen Dairy Group farms issued with ''restricted place'' notices in July, she said the original farm was identified because it had the Van Leeuwen's permission to release the information.
The Otago farm has also had a restricted place notice put on it, meaning all stock movement from it is restricted.
The three farms are the only ones to have such notices placed on them since the disease was discovered in New Zealand last month.
Federated Farmers Waimate branch chairman John Gregan said farmers wanted to know more about the farm that had been identified in Otago, as there was speculation and concern in the area about possible animal movements.
''Farmers and stock agents know who deal with each other. I'm sure there will be a lot of fingers being pointed at the moment.''
North Otago Federated Farmers dairy chairman Lyndon Strang told Radio New Zealand ''some respect the privacy of the farmer, others believe it is a bigger issue''.
In its 17th update on the disease to stakeholders, issued on Wednesday, MPI said it was ''aware of persistent rumours that there are other infected properties'', but said it was ''tracing all reports and at this time there are only three confirmed positive properties''.
MPI said the properties it was ''checking with urgency'' were 14 its investigations had shown received animals from the Otago property identified this week.
''There is a lot of other surveillance work under way ... but much of this is a routine and precautionary part of our disease response.''
DairyNZ chief executive Tim Mackle said MPI's response to the disease outbreak showed why the National Animal Identification and Tracing system was ''so important''.
