The Iceland international appeared to be on the verge of completing a £6.8 million switch to Swansea following a successful loan-spell in the second half of the season.
However Brendan Rodgers’ decision to leave the Liberty Stadium to fill the vacant managers position at Liverpool a fortnight ago has seen the deal stall.
Rodgers admitted that he wants to bring the 22-year-old to Anfield but refused to submit a formal bid for Sigurdsson’s services until he had spoken to Swansea and new boss Michael Laudrup.
Hoffenheim started their pre-season training on Monday but have told the former Reading man he has two-weeks in which to complete his transfer to England.
“Gylfi Sigurdsson will not be with TSG 1899 Hoffenheim for the start of pre-season. He has, after consultation, obtained a prolonged holiday until 30 June,” said a statement on the club’s official website.
“The club wants the 22-year-old to continue to secure a future in the Premier League.”
Head coach at the German side and former Liverpool defender Markus Babbel admits it is best if Sigurdsson is given time to assess his options and sort out a move.
“Gylfi wants to stay in England and is in negotiations there,” he said.
“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 June 30, he has done nothing then he will return to his pre-season with us. We have agreed this with him.”
Sigurdsson scored seven goals in 19 appearances after signing on a short-term loan deal with the Swans after dropping out of favour at Hoffenheim, where he still has two years to run on his contract after joining in 2010.