It emerged on Tuesday night that a deal worth up to £45million for Sigurdsson had been agreed, which would be a record transfer fee paid out by the Merseyside club, who are now 7/1 chances with Sky Bet to secure a top-four finish in the Premier League.
Gyfli underwent his medical this morning and Ronald Koeman confirmed in his press conference that everything went well and that a deal would be done shortly.
"I have seen the doctor and there is no problem", said Koeman.
"I think the way it's going there needs to be more than likely a compromise on both sides".
Sigurdsson was impressive for Swansea last season and played a big role in terms of helping the club to avoid relegation from the Premier League.
Only two other players, Manchester City's Kevin de Bruyne and Tottenham's Christian Eriksen, brought more goals and assists to their teams and Everton quickly targeted Sigurdsson as a key signing during a transfer window in which they have spent heavily.
"This is an ambitious club and it is clear we are moving in a really good direction". Having scored nine out of Swansea's 45 Premier League goals, the departure of Sigurdsson means that a significant portion of Swansea's firepower will now be lost.
Following their Europa League encounter at Goodison Park, Everton visit Manchester City in the league on Monday. I can say it is like maybe to p*** you off. I need to talk to him and know what his physical state is. It looks like a hamstring injury but we need to do more tests.to know exactly what the injury is.
Ramiro Funes Mori could miss the majority of the season with a knee injury leaving Koeman, who has been starting with three central defenders, short of cover at the back, while he had been linked with Arsenal forward Olivier Giroud in his quest to add a third forward.