The remaining 10 stores are still trading but the manufacturing facility, also in Orkney, is not taking on any new orders.
The Livingston shop was shuttered at the weekend, with a "small number" of job losses, when the landlord at The Centre in the West Lothian town used a break clause in the lease agreement.
James Stephen, joint administrator at BDO, suggested he "possibly wouldn't" have shut the premises if the clause had not been exercised.
In Orkney there were no job losses even though the shop at Hatston has been closed down. The Albert Street site remains open.
Mr Stephen said: "It was easier to house it under one roof [in Orkney] particularly when you are in quite a big sale mode."
The administrators signalled last month a sale of the whole business was unlikely.
Yesterday, Mr Stephen confirmed discussions with "various parties" over buying certain stores, the manufacturing facility, the brand and back catalogue of designs was still going on.
He said: "We are speaking to people with a variety of different interests. We have people interested in the manufacturing, the brand and certain stores. People interested in the brand and manufacturing without stores and we have got people interested in taking on some of the stores, presumably to do something different other than Ortak."
All the interest so far has come from the UK with some potential Scottish bidders among those taking a look at Ortak.
However the existing management team is not expected to form part of any bid.
The future of the remaining Ortak staff, thought to be around 100 people, is likely to be clearer by the end of this month. Mr Stephen said: "Over the next week or so we are trying to bring [the interest] to fruition to see if we have bids which are acceptable to us as administrators. Clearly if they are we would look to progress those.
"It is possible we might look at closing dates for certain aspects depending on the level of interest but really at the moment it is just ongoing discussions to firm up what people are genuinely interested in."
The manufacturing site on Orkney has now been closed to taking on new orders with Mr Stephen suggesting the current scope of work would run for a "couple of months".
He said: "We have been taking in new orders up until the end of last month but now we are focusing on converting the work in progress that we have got in the factory.
"There is a reasonable length of time in that."
Festive trading was said to have been "healthy" while a sale which started on January 11 was described as "very successful".
Mr Stephen said: "The [interested parties] are seeing the unit generates good sales. Whether they are going in to do an Ortak brand or something different [then] clearly the units are in good locations.
"We are still very active on our sale process and have a lot of stock to realise. We have discounted quite decently in our eyes and there is still a good range left."
Ortak, established in 1967 by Malcolm Gray, has been in administration since March last year after falling victim to the tough trading conditions on the high street.
A number of famous names have modelled for Ortak's collections in the past including Carol Smillie and her daughter Christie, Myleene Klass, Suzanne Shaw, Amanda Lamb and Kate Ford.