Main mill owner Derick Murray put his business up for sale in August with a price tag of £5m ($7.8m).
Interested companies have until Friday to lodge their bids for the KM Harris Tweed Group, which accounts for about 95% of total production of the fabric.
The selling agents said there had been a lot of interest in the group.
However, they would not confirm reports that a bid has been received from a major Turkish textile company.
The successful bidder will not be known for a number of weeks.
The Clo Mor - as Harris Tweed is known in Gaelic - can be woven only in the Outer Hebrides.
About 200 home-based island weavers are commissioned by the KM Harris Tweed Group to hand-weave 100% new wool which is spun, dyed and finished.
Cash aid
It is then returned to mills to be washed and marked and sent to buyers under the Harris Tweed trademark.
About 70 people are employed at the two mills, which are located at Stornoway and Shawbost on the Isle of Lewis.
The industry has been in decline since the mid 1980s, despite millions of pounds of cash aid.
It currently provides work for about 350 people, compared with more than 2,000 in its heyday.
However, the cloth is back in fashion and women's sales, in particular, are rising.
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