Sigurdsson, 27, has long been admired by Koeman and is eager to leave south Wales for Merseyside this summer, but Swansea are not prepared to let the Icelandic international leave cheaply, rejecting bids of £40m and £45m as they hold out for £50m.
"Of course we have interest in the player [Sigurdsson]," Koeman said in his press conference. Asked if Everton will return with another bid for Swansea's talisman, the Dutchman said: "I don't know, I don't know."
Everton have already made seven first-team signings this summer, with Koeman aiming to build a team capable of competing both in the Premier League and Europa League - a campaign which begins on Thursday [27 July] against Slovakian side Ruzomberok.
Despite the flurry of incomings Koeman is keen to see even more fresh faces arrive at Everton, with a centre-back and a striker high on his agenda due to the injury to Ramiro Funes Mori and the departure of Romelu Lukaku.
And quizzed over whether Everton's business is over for the summer, the Dutchman added: "I hope not. I don't speak about names, I think there are a lot of rumours. We lost Funes Mori, we're looking to replace him and we lost Lukaku, we brought Sandro Ramirez in and we're trying to get another striker in, and maybe one more."
Ramirez is not the only forward that Everton have signed this summer. Wayne Rooney returned to his boyhood club from Manchester United earlier this month and has impressed Koeman during his second spell on Merseyside.
There were some doubts over Rooney's capability due to his fading influence at Old Trafford - he started just 15 times in the Premier League last season - but Koeman said the decision to bring Rooney back to Goodison Park was an easy one.
"I met Wayne to talk about his situation and what he showed to me what was what i like and what we need," Koeman added. "There are no doubts over his quality, he is used to winning titles. It was an easy decision to advise the board to sign Wayne."