Relegation threatened Swansea are ready to cash in on the Iceland international after rejecting all offers for him following an impressive showing at Euro 2016 last summer.
Sigurdsson is keen on move on from South Wales even if Swansea are successful and maintain their Premier League status.
Everton boss Ronald Koeman tried to sign Sigurdsson after moving to Merseyside last year and has been keeping close eye on him all of this season.
Gylfi Sigurdsson is set to leave Swansea this summer Which 2016/17 Premier League stadium is oldest? Sat, April 15, 2017
Half the stadiums that will be used during the 2016/17 season were built after 1995, but which club has the oldest ground?
Play slideshow Getty Images 1 of 21
Which Premier League team plays in the oldest ground?
Ronald Koeman tried to sign the Swansea star last summer
He see’s Sigurdsson as an ideal replacement for Ross Barkley who is likely to move to Tottenham Hotspur before he goes into the last year of his current contract.
Newcastle United are also interested in Sigurdsson but Everton are in pole position with a huge offer which they will be unable to match.