Sigurdsson played under Brendan Rodgers at Swansea last season, while on loan from German side Hoffenheim.
He was expected to follow the new Liverpool boss to Anfield this summer after stalling on a £6.8m move to the Liberty Stadium when Rodgers departed.
The move to White Hart Lane is expected to be completed before the end of the week.
It is a blow for Liverpool as Rodgers seeks to strengthen his squad for a challenging new season.