Drinkwater has been linked with a move to Stamford Bridge for around £30million.
Bakayoko was signed earlier in the summer from Monaco and has made just two appearances as he makes his return from a knee injury.
But with the threat of increased competition, Bakayoko reckons Drinkwater’s potential arrival is a “good thing”.
He told French outlet SFR Sport: “Danny Drinkwater does not scare me. It is a very good thing!”
Chelsea have been after Drinkwater during the transfer window with boss Antonio Conte wanting to add strength and depth to his squad.
And on Saturday, Leicester boss Craig Shakespeare admitted he wasn’t sure whether he would be able to keep hold of his star names.
“It is difficult to say (if they will sign more players),” he said.
“We would like to and we will work hard behind the scenes and then we will see how it goes.
“I am pleased with what we have got but to add a couple would be great.
“In terms of outs, again it is difficult to say because we are not sure what other clubs will do.”
The move would reunite Drinkwater with N’Golo Kante, with whom he had an excellent on-field relationship as Leicester won the Premier League title in 2016.
Meanwhile, Chelsea are also closing in on England international winger Alex Oxlade-Chamberlain after agreeing a £35m fee with Arsenal.
Oxlade-Chamberlain is out of contract at the end of the season despite Arsene Wenger’s public insistence he would stay, he now looks set to join the Premier League champions before the transfer window closes.