The Toffees have been chasing the Iceland international throughout the summer and have already failed with one offer of £40million as Swansea dig in and refuse to let him leave for a penny less than their valuation.
Everton are believed to have gone back with an offer closer to £45million, but again it has been knocked back by the Swans, who will only cash in once a £50million offer has been made.
Sigurdsson has not travelled with the Swansea squad to the United States and has clearly set his heart on a move to Goodison Park, but that is of no concern to the Swans' hierarchy, who are refusing to budge.
Swansea owners Steve Kaplan and Jason Levien have issued a strongly worded statement, saying they will not sell unless they received an acceptable offer, thought to be £50million.
"We will not be bullied or forced into a decision until a club meets our valuation of the player, no matter whether they believe they have an agreement with the player," the statement read.