According to the bank, the potential buyers range from large European banks to smaller private equity firms interested in buying either the whole group or specific units individually.
However, spokesman Joerg Neef declined to mention any of the parties involved, except to confirm earlier press reports that German businessman Patrick Bettscheider was considering making an offer.
The news follows the resignation just a few days ago of Swissfirst's chief executive Thomas Matter.
He decided to step down in order to protect both the bank and his own personal interests from the fallout of insider trading allegations.
The allegations are linked to the merger of the bank last year to fellow Swiss bank Belle Vue - a scandal that prompted Swissfirst to put itself up for sale in the first place.
Analysts have suggested that the resignation could be a ploy to ensure that the sale of the bank goes smoothly.