Chelsea have spent almost £150million on signing Alvaro Morata, Antonio Rudiger and Bakayoko this summer but Conte is keen to add three of four new faces to his squad before the window closes.
According to Matt Law's report in the Telegraph, Chelsea have yet to follow-up on a rejected £15 million bid made "earlier in the window" for Leicester City for midfielder Danny Drinkwater, who's now sidelined with a thigh injury.
The Daily Telegraph is reporting that the west London side are ready to make another attempt to lure the 27-year-old midfielder to Stamford Bridge after failing with their first bid to sign the England worldwide.
The same article states that Chelsea had a bid of around £15m rejected by Leicester City this month as Antonio Conte looks to bolster his midfield options this summer.
The 27-year-old played a major role in helping the Foxes win the title in 2015/16 while he's also been recognised at worldwide level after breaking in to the England national team set-up.
A move to Stamford Bridge would see Drinkwater link up with N'Golo Kante once again.
As well as signing another central midfielder, the newspaper claims Conte is also looking to bring in at least one wing-back, an attacking midfielder and another forward over the coming weeks. Recruiting the former Manchester United starlet would also add to the club's share of "home-grown" players, which Conte is said to be keen on doing, but other than that the London Blues are best to focus on their other interests in proven players such as Oxlade-Chamberlain or Van Dijk.