Gylfi Sigurdsson has opted not to travel with his Swansea City teammates to the United States amid suggestions that Everton have submitted a bid for the Icelandic playmaker. Such an absence hints that both clubs may finally be entering the concluding stages of one of the summer's most high-profile Premier League transfer sagas.

Swansea confirmed on Thursday morning (13 July) that Sigurdsson, who returned to pre-season training earlier this week, would not travel to Philadelphia for an 11-day tour that includes matches against the Philadelphia Union, Richmond Kickers and North Carolina FC. That comes after he was handed the captain's armband on Wednesday evening for the second half of a 1-0 defeat at Barnet.

"Swansea City can confirm that Gylfi Sigurdsson will not travel with the squad to America for the pre-season tour," the club revealed via their official website.

"Having played against Barnet last night, Gylfi did not feel in the right frame of mind to travel this morning due to the current uncertainty over his future."

The confirmation followed reports from The Telegraph that Everton had seen an initial club-record offer of £40m ($51.6m) for the former Reading, Hoffenheim and Tottenham Hotspur midfielder rebuffed by Swansea. However, the same publication suggests that discussions will continue and that a deal could be completed as soon as this week.

Speaking after his side's loss at The Hive Stadium, Clement conceded that Sigurdsson could follow new Burnley signing Jack Cork out of South Wales if his valuation is met. Swansea have also offloaded the likes of Bafetimbi Gomis, Borja Baston and Jordi Amat over recent weeks while bringing in Tammy Abraham, Roque Mesa and Erwin Mulder.

"I've made it very clear I want him to stay here," Clement said, one day after acknowledging there was "very strong interest" mounting in a player who previously insisted that he was not desperate to leave. "The fans want that, the owners would like that but, ultimately, there's a business side to football as well.

"We had that situation with Jack Cork. In the summer there was no thought of moving Jack on but it got to a point when another club came in with a really good offer. That might end up being the case with Gylfi. We don't know yet."

Leicester City have also stepped up their interest in Sigurdsson since confirming Craig Shakespeare as their permanent manager last month, with the BBC claiming last week that the Foxes had also failed with a £40m bid as Swansea hold out for £50m.

Sigurdsson signed a new four-year contract in August 2016 before scoring 10 goals and providing 13 assists in 40 appearances across all competitions to help the 2013 League Cup winners end a tumultuous campaign by avoiding relegation to the Championship.

Gylfi Sigurdsson
Gylfi Sigurdsson captained Swansea during a 45-minute cameo at Barnet on Wednesday night Nigel Roddis/Getty Images