Barkley, 23, is set to leave his boyhood club this summer after rejecting a lucrative contract offer earlier this year, with Koeman confirming that the vaunted England international is looking for a 'new challenge'.
Everton have already gone some way to replacing Barkley this summer; Netherlands international Davy Klaassen has arrived from Ajax for around £24m while Swansea City's Gylfi Sigurdsson is expected to arrive on Merseyside in the coming weeks.
The Merseysiders placed a £50m price tag on Barkley a few months ago, but Tottenham are understandably reluctant to pay such a fee for a player who is in the last year of his contract with a burning desire to leave. Spurs are instead hoping to strike a deal worth around £25m, though Koeman said there are no offers for Barkley at present.
Despite the impending exit of Barkley to Tottenham and the departure of star striker Romelu Lukaku to Manchester United, there is a feelgood factor surrounding Everton, partly down to their impressive summer signings.
Koeman has substantially strengthened his side with seven new additions and has made no secret of his desire to sign Sigurdsson, a new centre-forward and a left-sided central defender before the window closes. Ideally Everton would have signed their remaining targets by now, but Koeman accepts that is not always possible.
"It is not about Ross [Barkley]," Koeman told The Liverpool Echo. "We did really good work and I didn't expect to get all the players in before tomorrow, some need more time and that's all about business.
"I'm still not nervous and we have time but we have enough new players in. But, okay, everybody knows that we have tried to get one or two more in."
Everton have already signed three forwards this summer in the form of Wayne Rooney, Sandro Ramirez and Henry Onyekuru, but Koeman is intent on bolstering his strikeforce further in order to contend with the loss of Lukaku. Olivier Giroud, Edin Dzeko and Christian Benteke have all been linked, and Koeman admits one forward in particular is on his mind.
"We try the best we can get, it is all about qualities, about qualities of the striker, playing alongside Sandro is also a possibility," Koeman added. "I know which one I like - but whether we (get him)...that's difficult."
Koeman's quest for a forward is not over yet, but Everton have completed the signing of Newcastle United starlet Lewis Gibson for around £6m. The teenage defender, who can operate at centre-half or left-back, will join up with David Unsworth's Under-23 side.