The Toffees have been linked with the Iceland international for some time now, having a £25million offer knocked back by the Swans last summer.
But now, Swansea have increased their valuation to a staggering £40million, such is his importance to the South Wales side.
Swansea have been on the record saying that they have no intention of selling their star man this summer, and Sigurdsson’s agent has also claimed that his client is happy with his current situation.
However, Ronald Koeman views Sigurdsson as the ideal candidate to replace Ross Barkley this summer, with the Evertonian looking ever the more likely to depart the club.
After having already broken their transfer record with the £30million signing of Jordan Pickford this past week, the club may have to do so again if they are to land the 27-year old attacking midfielder.