Everton have already signed a playmaker in Davy Klaassen this summer but Koeman is looking to add more depth to that position.
According to Daily Mirror, the Merseyside outfit are looking to sign the Swansea midfielder Gylfi Sigurdsson and have already submitted a £30 million bid for the Iceland international.
The report adds that Swansea have rejected the offer and it seems that the Welsh club will only sell the player if their valuation is met. It will be interesting to see if Koeman returns with an improved offer now.
The Toffees have already splashed out on the likes of Pickford and Klaassen.