Having already strengthened the backline with the addition of Steven Caulker, Brendan Rodgers looks to be in the market to add another defender to challenge for a centre back berth.
Vorsah, who can also play as a defensive midfielder, starred in the Bundesliga last year and is also being tracked by Borrusia Monchengladbach.
A regular for the Ghana international team, he won the defender of the year award for his country in 2007 and earned rave reviews for his performances in the 2010 World Cup.
The 23 year old is also being linked with a move to Hoffenheim's Bundesliga rivals Borussia Dortmund, but the Swans look to be favourites after Deutsche Welle TV reported that officials were meeting to agree on a deal.