Everton are reportedly closing in on signing Sigurdsson, who was valued at around £10 million by Tottenham when he left the club in 2014, after agreeing a deal with Swansea worth up to £45m for the playmaker.
The Iceland midfielder is expected on Merseyside on Tuesday evening and will undergo a medical at Goodison Park on Wednesday.
Sigurdsson pulled out of Swansea's pre-season tour to the United States after Everton's interest had become clear.
They have already turned down two bids from Everton and rejected a reported £40m offer one from 2016 champions Leicester at the beginning of the summer.
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Everton were keen to tie up the swoop before the transfer window closes at the end of August and it is believed Swansea have at last agreed to sell their prize asset.
Clement said: "We're at a critical stage and hope it's going to be resolved as soon as possible".
The 27-year old was integral to Swansea retaining their Premier League status for another season, and his productive campaign saw only Kevin De Bruyne and Christian Eriksen, two of the league's chief creators, record more assists.
His form has convinced Everton chiefs to splash out on Sigurdsson, adding to Wayne Rooney, Jordan Pickford, Davy Klaassen, Michael Keane, Cuco Martina and Sandro Ramirez all joining the Toffees.
Manchester City striker Wilfried Bony, West Brom forward Nacer Chadli and Stoke midfielder Joe Allen have all been linked with Swansea.
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