Priskin struck 14 times for Watford in the 2008/09 season when now Swans boss Brendan Rodgers was in charge.
Swansea have already bolstered their strike force with Chelsea's Fabio Borini who scored twice on his debut in the 3-2 win over Nottingham Forest.
The emergency loan window closes at 1700 GMT on Thursday.
Source: BBC Sport
Source: BBC Sport