Speaking on LTV's Rita Panorama morning news show, Straujuma refused to name the investor believed to be mulling an offer for the bank, but did confirm that a single potential buyer is being offered the chance to make a purchase on an exclusive basis, instead of via an open tender.
LTV and other media have for several weeks reported that the exclusive investor is US-based investment vehicle Ripplewood Holdings and the price asked by the government is around 113m euros.
So far, most government discussions on the matter of selling Citadele have been held behind closed doors.
The unnamed investor has been given an August 25 deadline, but that date might be extended by ten days, raising the possibility that a sale could be completed before parliamentary elections on October 4.
"Selling the bank in good condition is important, but the key is to find a good investor who, via their investment, will be able to bring further stability to the Latvian banking system," Straujuma said.
Citadele was formed from part of the wreckage of the notorious Parex bank, whose collapse in 2008 forced Latvia to seek a bail-out from the International Monetary Fund.
The Latvian state owns 75% of Citadele with the remainder owned by the European Bank for Reconstruction and Development.