The Toffees were knocked back with their initial bid of £40m, and Sky Sports understands that their addition of £5m worth of add-ons has also be denied.
The Iceland midfielder was left off the Swans 10-day USA tour because he was not in "the right frame of mind to travel."
Swansea are believed to be holding out for a fee of £50m for their star player.
The 27-year old has been the club's talisman since he joined from Tottenham in 2014 for £6.8m, scoring 37 goals in 131 appearances.
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