Conte plans to line-up with new signing Tiemoue Bakayoko and last season player of the year N'Golo Kante.
And Conte is keen to secure England worldwide Drinkwater as soon as possible, with the Blues kicking off their title defence against Burnley on August 12.
The 27-year-old is a product of Man Utd's youth academy but has made his name since joining Leicester City in 2012 as he played his part in helping the Foxes secure a stunning Premier League title win in 2015/16.
Leicester City would (and should) hope that Chelsea aren't too serious about their pursuit of Danny Drinkwater, because if they are, then the lure of the Bridge would mean there's only one victor.
Today, Chelsea are linked with Danny Drinkwater...
"Drinkwater is now priced at 2/1 with BetStars to join the Premier League champions this summer".
Leicester are firm with their stance that Drinkwater - who only signed a new four-year contract at the club in 2016 - is not for sale, however.
The Italian Manager has already asked Bayern Munich about the availability of Renato Sanches and Drinkwater is also on his list of targets.
The Italian tactician believes his squad is still short of the depth it needs this season, with the Blues back in the Champions League after winning the title last term, when their lack of European football meant they could play the same starting line up nearly every week.