Swansea City have questioned whether Everton have approached Gylfi Sigurdsson and warned they will not be bullied into dropping their £50m asking price for the Iceland midfielder.

Sigurdsson stunned Swansea officials and coaching staff on Thursday when he pulled out of the club’s trip to the United States shortly before the flight to Philadelphia. The 27-year-old was apparently “not in the right frame of mind” amid continued interest from Everton, who want him as part of their summer spending spree.

Everton have had a £40m package for Sigurdsson rejected this week. Swansea value their player of the year at £50m and in a statement issued on behalf of the owners Steve Kaplan and Jason Levien made it clear the price would not alter despite Sigurdsson’s stance.

Swansea also encouraged their most influential player to reconsider his decision not to join the US trip and, in echoes of Southampton’s reaction to Liverpool’s pursuit of Virgil van Dijk, suggested Everton may have contravened Premier League rules with an illegal approach.

The statement read: “We are disappointed Gylfi has taken the decision not to join his team-mates in America where they are working with the coaching staff to prepare for the upcoming season. At this time we have not received an offer from any club which represents a fair valuation of Gylfi given his importance to our club.

“As we have stated, 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. Any such agreement would obviously be in contravention of Premier League legislation. We have the ultimate respect for Gylfi as a person and a player and we are optimistic that he will reconsider his decision and join his team-mates.”

Ronald Koeman wants his new-look Everton squad in place quickly, with the first competitive game of the season less than a fortnight away. Everton have been drawn to play Ruzomberok of Slovakia or Brann Bergen in the third qualifying round of the Europa League. The Norwegian club won the first leg 1-0 and Everton will be at home in the first leg on 27 July.