Although Chelsea have brought in Tiemoue Bakayoko to replace their Serbian midfielder, they are well short of numbers on the bench, with just 14 experienced players available.
Chelsea will reportedly launch a second bid for Leicester City midfield playmaker Danny Drinkwater after previously having an offer of around £15 million rejected.
However, the Blues boss knows he needs to further strengthen if Chelsea are going to compete on all fronts this season and the Evening Standard claims director Marina Granovskaia has stepped-up the clubs pursuit of new players with Conte wanting up to four more new arrivals before the end of the month.
It remains to be seen whether Chelsea will be prepared to pay that kind of money but Drinkwater would provide solid competition for the likes of Bakayoko, N'Golo Kante and Cesc Fabregas if he were to move to Stamford Bridge and he'd also boost the clubs homegrown quota.
There have been widespread reports in the British media in recent days suggesting that the Blues are keen on luring the England worldwide to Stamford Bridge following the sale of Nemanja Matic to Manchester United last week.More news: Everton confirm four out of Stoke clash, one returning, six possible debuts
The report says Chelsea are set to return with a significantly larger bid in the region of £25m. 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.
However, the England global is reportedly not concerned and is keen to test himself at Stamford Bridge.
Craig Shakespeare has poured cold water on talk of Chelsea signing Danny Drinkwater from Leicester City this summer..
With three weeks of the transfer window remaining, a handful of Foxes stars have been linked with other clubs.