The Toffees saw a £40m bid for Sigurdsson rejected earlier this summer but appear to have finally struck a deal with the Swans holding out for £50m.
Koeman's side have been one of the active in the summer window, having added Michael Keane, Davy Klaassen, Jordan Pickford, Sandro Ramirez Wayne Rooney and Cuco Martina to their squad.
And it seems Icelandic international Sigurdsson is next.
"We are close (on Sigurdsson), we have to wait... the deal is not done," Koeman said after Everton's 2-2 with Sevilla on Sunday.
"Everybody knows we are looking for three more players - a left centre-back, a left full-back, a player who can play out of both positions, a winger and a striker and that's the picture, what the best is for our team and we will see what we can do."
Winger Aaron Lennon was not included in the Everton's squad in their last pre-season friendly against the Spanish side. He has been linked with a move to Watford but Koeman said the club have received no offers for the 30-year-old.
"The reason that he wasn't in the squad is that he was not fit to play today. I don't know about any interest for Aaron, I don't know," the Dutchman added.
Koeman's side host Stoke City at Goodison Park in their opening game of the league season on Saturday.
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