The Southampton boss is expected to take the reins at Goodison Park this week.
Koeman's Saints departure is all but confirmed
The Saints are said to be holding out for £5 million in compensation for Koeman, who has agreed to replace Roberto Martinez at Goodison Park.
However, the report claims that while the Toffees have agreed to pay the remainder of the Dutchman's £3.5 million-a-year contract, the delay relates to the release of two key aides.
Southampton are said to want a further £1.5 million for Koeman's brother, Erwin, and fitness coach Jan Kluitenberg - who worked with the 53-year-old at AZ Alkmaar and Feyenoord, and followed him to Saints in 2014.
The Koeman brothers were reunited at St. Mary's
Erwin Koeman, who is the older of the two siblings, is expected to assist the new Everton boss, having worked with him for the first time - from a coaching point of view - at St. Mary's.
The report contains no mention of Koeman's first team coach Sammy Lee, whose strong Liverpool connections have caused some concern among the Everton faithful.
Most Evertonians aren't keen on the idea of Lee (centre) following Koeman to Goodison
Koeman was suggested as the Toffees' leading choice at the time of Martinez's sacking four weeks ago, but later admitted he expected to see out the final year of his contract at Southampton.
However, Everton's reported £7 million-a-year offer, along with the promise of significant transfer funds, is said to have proved decisive.
Farhad Moshiri is said to have offered Koeman sizeable funds to play with