Sky sources understand there has not been any contact between the two clubs about the potential deal yet.
Sky Sports’ Guillem Balague understands that Conte wants to sign Llorente “for sure”, while Sky in Italy are saying a swap deal involving Batshuayi is “moving closer”.
It is not clear if the deal would see the players moving permanently, or on loan, or one permanent and one loan
Conte knows Llorente well, having coached him at Juventus and the pair won the Serie A title together in 2014.
Spaniard Llorente has scored six goals in 17 Premier League appearances for the struggling Swans this season.
Belgian Batshuayi is yet to start a Premier League game since arriving from Marseille in a £33m move last summer. He did play – and score – in Sunday’s 4-1 win over Peterborough in the FA Cup third round.
Asked on Sunday about the reports from Italy about the potential swap, Conte said: “I repeat always in the same, in this period – I don’t like to talk about players of the other teams because it is not respectful to the player and for the team.”