Press Association Sport understands a fee of £5million has been mentioned even though the 53-year-old has only one year left on his remaining contract.
There is unlikely to be any breakthrough until Tuesday at the earliest while dialogue continue between the two clubs.
Once that has been completed getting Koeman to agree personal terms may be slightly easier, although the chances of actually seeing the Dutchman on Merseyside appear slim as, according to reports in his homeland, Koeman has gone on holiday again.
He has left his agent Rob Jansen to take care of his interests while he is away and it will be he who negotiates the final package with Everton chairman Bill Kenwright and majority shareholder Farhad Moshiri when Everton are given permission to speak to Koeman by Southampton.
Everton are also understood to be keen to recruit Sevilla's sporting director Monchi to undertake a similar role at Goodison Park once Koeman's appointment has been confirmed.
The 53-year-old has helped make the Spanish club a significant profit in the transfer market during his 15-year spell in the job after securing top fees for players with untapped potential, while also contributing to five Europa League victories in the past decade.
It is believed Sevilla would require £3.8million to trigger Monchi's release but that is unlikely to deter Everton, backed by Iranian billionaire Moshiri who has reportedly set aside a £100million transfer war chest for the new manager.
Source : PA
Source: PA