The 27-year-old has established a reputation as a solid deep-lying midfielder and he helped Leicester win the title last May.
A year ago his performances under then-Foxes boss Claudio Ranieri saw him linked with a return to boyhood club Manchester United.
Drinkwater stayed at the King Power Stadium though and was one of Leicester’s most consistent performers amid their broader struggles last season.
It seems his form caught the eye of Chelsea gaffer Antonio Conte, who’s keen to bolster his squad before the transfer window shuts.
The Blues have already added Tiemoue Bakayoko to their ranks this summer.
However his injury woes, Nemanja Matic’s departure and Cesc Fabregas’ suspension mean they are light in midfield going into this Sunday’s visit to Tottenham.
Conte therefore wants to get Drinkwater on-board as soon as possible and The Telegraph claim that will see Chelsea up their bid for him.
Leicester have already knocked back a £15m offer and are likely to be unmoved if that is increased by £10m as the newspaper suggest.
The Telegraph reckon Leicester are holding out for £40m - the figure which took Matic to Manchester United at the end of last month.
Drinkwater’s price tag is based on his age, the fact he is under contract until 2021 and his status as a homegrown player.
And it remains to be seen whether Chelsea chiefs will value him as highly and be prepared to sanction a deal for that much.
