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The 27-year-old, due to sign a five-year contract worth £100,000 a week, would be Everton’s record signing, topping the £31.8 million they paid Chelsea for Romelu Lukaku in 2014.
“I have seen the doctor and there is no problem,” said Koeman at a press conference on the eve of their Europa League match with Hakjduk Split.
“Still he needs to sign, but I saw him in the blue!”
Sigurdsson, who played a pivotal role in Swansea retaining their Premier League status last term after scoring nine goals and creating 13, pulled out of their pre-season tour to the United States and was not included in the squad for last weekend’s 0-0 draw with Southampton.
Swansea, who are also battling to keep Chelsea target and veteran Spanish striker Fernando Llorente, had wanted £50 million.
They have already turned down two bids from Everton and rejected a reported £40 million offer from 2016 champions Leicester City at the beginning of the summer.
It is believed, though, that Everton will get their way in paying an initial £40 million with another £5 million to follow, taking their summer spending under Koeman to over £140 million.
Everton’s majority shareholder Farhad Moshiri has spent close to £100 million so far in recruiting former favourite Wayne Rooney, goalkeeper Jordan Pickford (£30m), midfielder Davy Klaassen (£23.6m), defender Michael Keane (£30m), Cuco Martina and Sandro Ramirez.
However, a considerable proportion of the spending has been financed by the £75 million sale of Lukaku to Manchester United.
“We worked a long time to get this deal in and he was one of the key players to bring in,” Koeman said.
“We knew we would lose (Romelu) Lukaku for this season, with that we lost 25 goals, and we need players who will bring in productivity to the team.
“He is that type of player, with a lot of productivity.”
Everton could further balance the books with a big money sale of midfielder Ross Barkley to Tottenham Hotspur, although he is currently injured and likely to be out until October.
Koeman was not very forthcoming when asked about Barkley’s situation and his long-term future at the club.
“He stopped training last Monday,” said Koeman.
“It looks like a hamstring injury but he needs to do more tests today and tomorrow to know exactly what the injury is.
“I will wait until the end of August,” he added when asked about Barkley’s future at the club.
Icelandic international Sigurdsson finished third in combined goals and assists amongst midfielders in the Premier League last season behind Manchester City’s Kevin De Bruyne and Tottenham’s Christian Eriksen.
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