The group snapped up the Scottish agency, which currently has 13 stores, in March 2012.
However, Minoan announced in March it was now looking to dispose of Stewart.
In March, it confirmed an exclusive agreement had been reached with a preferred buyer.
Chairman Christopher Egleton added, in an April trading update, its decision to dispose of its travel arm “had not been taken lightly”.
A fresh trading update from Minoan, issued on Monday morning (July 2), intimated the sale was now imminent.
“The board expects the company will be in a position to exchange contracts in respect of the sale of STL [Stewart] in the next few weeks,” it read.
“Further, it understands no issues have arisen during financial and commercial due diligence.
“A general meeting will be called immediately after exchange in order that shareholders can approve the transaction.”
Minoan, meanwhile, says it is in discussions with Hillside International Holdings Limited over its debt facility.
The group last year agreed an extension until June 30, which has now lapsed.
Minoan though says it is in discussion with Hillside with a view to extending this pending the successful sale of Stewart, providing the funds to settle the Hillside facility.