The Toffees splashed £26m to lure Klaassen to Goodison Park and it seemed that no more midfielders would be targeted by manager Ronald Koeman, but it is understood that Sigurdsson is still the main target this summer.
Everton have been after the Swansea playmaker since last summer but the Welsh club have been standing firm and are determined to hold on to their star man.
Sigurdsson was the key man to help Swansea escape relegation last season by scoring nine goals and providing 13 assists, many of which were to teammate Fernando Llorente who he has formed a formidable partnership with.
The 27-year-old has not commented on what he would like to do, but he does want to make sure he is starting consistently in the Premier League as when he was at Tottenham Hotspur, he struggled for game time.
Therefore the signing of Klaassen puts doubt over whether Sigurdsson would start every game at Goodison Park. The continued interest in the Iceland number 10 does cast doubt on the future of Ross Barkley at Everton who could be leaving the Merseyside club this summer.
Everton’s finances took a huge boost following the takeover by Farhad Moshiri and by potentially selling Belgian striker Romelu Lukaku they could fund the move for Sigurdsson.