However, Swansea released a statement stating no contact has been made from the London club regarding Llorente, who has only been at the Liberty Stadium since last summer after joining on a free transfer from Spanish side Sevilla.
Michy Batshuayi would prefer to join West Ham over Swanseahttps://t.co/InPRT9pwcB— Dean Jones (@DeanJonesBR) January 9, 2017
Llorente has netted six goals for Swansea so far this season, while Batshuayi is yet to start a game in the Premier League for Chelsea since his £33m move from Marseille last July.
Swansea boss Paul Clement spoke after his side's 2-0 defeat away to Hull in the FA Cup 3rd round, he said he wasn't aware of any deal in place to take Llorente to London.
Although Batshuayi's preference to stay in the capital may dash any hopes of Conte signing Llorente during the January transfer window.
Officials from Chelsea confirmed they have no plans to let the 23-year-old leave the club this month but their interest in Llorente is believed to be concrete and a bid could be lodged for the Spaniard very soon.