Llorente is believed to be the subject of interest from Chelsea, while Sigurdsson has also been linked with a move away from the Liberty Stadium after impressing in a struggling team this season.
Newly-appointed Clement, however, 'wants to keep his best players' at the club and will fight off any bids that arrive for the in-demand duo.
"[Llorente] is a very good player," Clement told reporters. "He has experience of playing football at the highest level. He has been linked with a move but there's been no contact.
"It's similar with Gylfi Sigurdsson. We are in a situation where we need to win games and to do that you need your best players here. You want to keep your best players and they are two of the best players here, so absolutely we want to keep them."
Swansea will enter Saturday's Premier League clash with Arsenal down in 19th position in the table - two points above basement side Hull City.