The Iceland midfielder had reportedly attracted interest from Manchester United after a successful loan spell at the Liberty Stadium but could now be set for permanent switch
The Iceland international joined the Swans on loan in January and scored seven goals in 17 appearances as Brendan Rodgers' side secured a comfortable mid-table finish in the Premier League.
The German side rejected Swansea's initial bid, thought to be in the region of €5m, but have now apparently allowed Sigurdsson to hold talks to remain at the Liberty Stadium.
The attacking midfielder's excellent form for the Swans was thought to have caught the eye of Manchester United manager Sir Alex Ferguson as the Red Devils seek to bolster their midfield.
Huw Jenkins, Swansea chairman, had confessed he thought it would be difficult to keep hold of Sigurdsson but the Icelander had insisted he would be happy to sign for the Swans permanently in April.
Sigurdsson began his career at Reading before joining Hoffenheim in 2010 but had fallen down the pecking order before his move to south Wales.