That is according to pundit and former West Ham defender Tony Gale.
Drinkwater has handed in a transfer request at Leicester in an attempt to force through a move to Chelsea.
Chelsea have had a £23million bid rejected for the England midfielder, with the Foxes holding out for northwards of £30million.
Drinkwater would be the second midfielder signed by Blues boss Antonio Conte this summer, following the arrival of Tiemoue Bakayoko from Monaco for £40million.
However, Drinkwater’s experience in the English top-flight with Leicester is something Bakayoko has not got, which is important according to Gale.
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“He (Bakayoko) hasn’t got the Premier League experience that Danny Drinkwater has got,” Gale said on Sky Sports.
“Danny Drinkwater will go in there seamlessly for me. He knows (N’Golo) Kante’s game inside out, he knows the Premier League inside out.”
Antonio Conte has allowed two central midfielders leave the club this summer, with Nemanja Matic joining Manchester United and Nathaniel Chalobah signing for Watford.
It is the latter deal which has confused Gale, who thinks Chalobah could have become a key player for the Blues.
“It was strange, Chalobah for me would have been perfect,” Gale added.
“He’s gone to Watford, Watford have nicked him.
“I saw him play at the weekend, Watford Brighton, that kid is going to be excellent.
“I think Chelsea have made a mistake by selling him.”