The former Liverpool player has revealed that he expects the 22-year-old to complete his transfer to England this week, but refused to specify which club he would be joining
The Iceland international impressed while on loan at Swansea in the second half of last season but stalled over a permanent deal when Brendan Rodgers left the club for Liverpool.
Rodgers was eager to re-unite with Sigurdsson at Anfield but, despite extensive talks, the 22-year-old is expected to now sign a deal with Tottenham in the coming days.
Following the speculation, the Hoffenheim boss has now revealed that a move is close to finalisation, but would not state his specific destination.
"Gylfi Sigurdsson is nearing agreement with a Premier League club," Babbel told Hoffenheim's official website. "It's all about the final details. I am assuming that the transfer will be completed by the end of the week."
Sigurdsson made 19 appearances and scored seven goals for the Swans after joining on loan in January and was elected as Premier League Player of the Month in March.