Everton were willing to pay to pay a big fee for the Sigurdsson, but Swansea value their star play maker at £50 million.
However, Koeman denies that negotiations have broken down, and insists that Everton still have a good chance of landing the 28-year-old this summer.
“It is still close,” Koeman revealed at his latest press conference. “That has not changed. I heard some rumours that the talks broke down but we are still in negotiations with Swansea. I have heard the comments of Paul Clement, the manager of Swansea.
“Everybody knows the window is difficult and it is always a game between the selling club and the buying club. But we are close. Let's hope we get an agreement as soon as possible.”
Everton have already done some eye catching business this summer, with confidence high around Goodison Park.
The Toffees have bolstered their squad with some brilliant additions, and more new arrivals are set to follow in the coming weeks.
Everton have made no secret of their desire to break into the top four in the coming years, and their signings have outlined their intentions to climb up the Premier League table.
Koeman’s side begin their league campaign tomorrow, when they play host to Stoke City.