The two players are key to Swansea, and while both have been linked with moves away, the club is keen to keep them in Wales.
Swansea City's Fernando Llorente celebrates scoring their fifth goal with Gylfi Sigurdsson
Swansea City chairman Huw Jenkins has claimed that there have been no bids lodged for either Gylfi Sigurdsson or Fernando Llorente, and that the club have every intention of keeping the pair for next season, as reported by Wales Online.
Wales Online also claimed that that Everton are one of a number of interested parties in Sigurdsson, who scored nine goals and claimed 13 assists for the Swans in the Premier League, while in January, Chelsea were knocked back in their attempts to sign Llorente, as reported by the Metro.
The 32-year-old striker hit 15 goals for Swansea in the Premier League, and worked with Chelsea boss Antonio Conte at Juventus, but a loan switch to Stamford Bridge was rejected by the Swans, who needed the Spain international for their relegation battle at the time.
Speaking about the duo's future at the Liberty Stadium, Jenkins insisted he was keen to keep the pair at the club and claimed that no offers have been submitted for either of the two, and also said that the club aren't in a hurry to sell their better players.
Swansea City's Fernando Llorente celebrates scoring their first goal (R) with Gylfi Sigurdsson
"When you look at the Premier League these things happen with players being linked with clubs," Jenkins, as reported by Wales Online. "Llorente had such a good season, it has worked well for him and the club after his season with Sevilla, where he did not play as much as he would have liked.
"With Gylfi we know how he helps our team with his assists and goals, he is a dead-ball specialist and has caused a lot of problems for opponents and won a lot of headlines. When a player does that someone will pick up on it and talk about players being wanted by other clubs in the Premier League. That will always happen.
"But there is nobody seriously coming knocking on our door, putting bids in or pushing things. We have said it before, we are not actively trying to sell players, and that will continue."
Swansea City's Gylfi Sigurdsson and Fernando Llorente celebrate at the end of the match
The 2016/17 season was a rough ride for Swansea, who had three permanent managers in one season, though it worked out for them in the end and relegation was avoided under Paul Clement's stewardship.
The Swans finished the season in 15th place - seven points clear of safety, and only five points behind eighth placed Southampton as a cluster of teams fought it out in mid-table.