PA PhotosSigurdsson enjoyed a hugely successful loan spell with Swansea last season, scoring seven goals in 18 appearances for the club.
His former manager Brendan Rodgers is known to be keen to bring him to Liverpool while Tottenham are also reported to have made an offer for the Iceland international.
Hoffenheim coach Markus Babbel confirmed on Monday that the 22-year-old is close to making a decision.
"Gylfi Sigurdsson is nearing agreement with a Premier League club," Babbel told the club's official website. "It's all about the final details."
