Hoffenheim has given midfielder
However, the departure of manager
Last week Rodgers admitted he would be interested in signing the midfielder but stressed the player had to first speak to Swansea - which appointed Michael Laudrup as its new boss on Friday.
Sigurdsson's German club, who began pre-season training on Monday, have granted extended leave in order for him to complete a move to
"He has, after consultation, obtained a prolonged holiday until 30 June.
"The club wants the 22-year-old to continue to secure a future in the Premier League."
Hoffenheim head coach and former Liverpool defender
"Gylfi wants to stay in
"Thus it makes no sense for both sides for him to return to Hoffenheim, perhaps only for a few days.
"If, by the deadline on
"We have agreed this with him."
Sigurdsson is contracted to Hoffenheim for another two years but despite impressing in his first campaign in 2010-2011 he dropped down the pecking order last season, forcing his loan to Swansea where he scored seven goals in 19 appearances.
It has been reported Liverpool will have to pay a fee in the region of £8 million ($12.39 million) as Swansea had negotiated a lower figure as part of its loan deal.
Arsenal's 1-0 Premier League victory over Newcastle United ensured it beat north London rival Tottenham Hotspur to the last UEFA Champions League place despite a late blockbuster from Gareth Bale on the final day of the season.