The Iceland global has been a target for Everton all summer with the Swans having already knocked back a reported £40million bid.
"He continues to train with the first-team [but] there is no deal done between us and any other club so the situation is as it was".
Aaron Lennon was absent from the squad for Everton's final pre-season fixture ahead of their Premier League opener against Stoke this Saturday.
But Swans manager Paul Clement insists that there has been no movement on Sigurdsson's situation since he delivered a previous update on Wednesday.
"No change since we last spoke".
The former Spurs player has scored 30 goals in all competitions for Swansea, while Barkley, the man he would likely be replacing, has scored 27 since 2010. "All parties would like it resolved", the Swansea boss told Sky Sports.
"I have heard that rumour every day since I joined Swansea", Clement said of the Blues' reported Llorente pursuit.
"But my focus is on the players I'm working with and getting ready for the season".
The 30-year-old France global had to make do with a peripheral role in north London last season and his chances of game-time have decreased further after Arsenal signed his compatriot Alexandre Lacazette for a club-record fee.
"Sigurdsson is one of those you cannot sell, you just cannot., but the problem you've got is if the player wants to go and they [another club] come up with the massive amount of money, which is £50m, then there's really nothing you can do".