Llorente starred for the Swans yesterday, bagging a brace in the Welsh side's 3-2 win over Liverpool.
Antonio Conte wants to bring the 31-year-old to Stamford Bridge to provide cover for Diego Costa.
Fernando Llorente is happy at Swansea despite interest from Chelsea
But Llorente admits he is happy at Swansea and wants to help the club stay in the Premier League.
“I am very happy here and I want to play and score more goals," Llorente said.
“I wanted to celebrate with the fans and say thank you. The goals meant a lot to me and it is an amazing feeling to score twice in one of the best stadiums in the Premier League against one of the best teams – but the fans deserve this feeling too because it has been tough for them.
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Fernando Llorente has thanked Swansea's fans for their support after the win at Liverpool
“I want to thank them for their support in some difficult moments and we know we must win more matches.
“It is important that we have feeling when we are on the pitch and they are in the stand. We are all together.
“But we must do more now. We know we can play very well, we have shown that at Anfield, and we have to continue and go on.
“We will continue to work in this way, it was a good performance for us and we will keep fighting.”