The former Athletic Bilbao man played some of his best football in Turin while Conte was there and has proved a good fit in the Premier League as well, per WhoScored.com:
Chelsea could use another striker for depth, with Diego Costa seemingly no longer an option, and Llorente and Alvaro Morata worked well together in the past. The veteran forward would also bring a brand of physicality off the bench that the Blues lack up top.
Swansea are said to be closing in on a deal for former striker Wilfried Bony, and if the Ivorian does return to Wales from Manchester City, it would be easier to part with Llorente. Per the report, the Liberty Stadium club previously were reluctant to deal.
Their asking price could be a major sticking point, however, as Delaney reported Swansea are still looking for £30 million for the 32-year-old.
Along with a striker, Conte is also said to be looking at midfield options and another wing-back. Drinkwater heads the list of possible candidates for the centre of the pitch, and Arsenal's Alex Oxlade-Chamberlain and Southampton's Cedric Soares are also mentioned.
Drinkwater has been linked with the Blues for some time now, and per Matt Law of the Daily Telegraph, negotiations have been ongoing for a while:
The 27-year-old played a big role in Leicester's surprise Premier League title win in the 2015-16 campaign but isn't seen as a major upgrade to Chelsea's current options. He would qualify as a homegrown player, however, partly explaining the club's interest.
With Nemanja Matic plying his trade for Manchester United, the Blues are short of options in the centre of the pitch, and a defensive specialist is needed. Drinkwater is versatile enough to fill that role or even push further up the pitch if needed.
The Blues have left it late in the transfer window to strike a deal for the Foxes star or Llorente, though, handing the leverage to their current clubs.