Kovacic is set to complete a season-long loan move to Stamford Bridge as he looks to earn more minutes than have been on offer to him at Santiago Bernabeu.
There will not, however, be any obligation to buy inserted into the deal, meaning as things stand Kovacic would return to the Spanish capital at the end of the campaign.
His arrival in west London is set to push Bakayoko further down the pecking order following a disappointing debut campaign in 2017-18.
The France international struggled to establish himself under Antonio Conte upon his £40 million ($51.7m) arrival from Monaco, and Goal understands intermediaries from the Blues have met with Rossoneri officials to secure a move for the 23-year-old.
His replacement, Kovacic, arrives following Maurizio Sarri's request that the club sign a midfielder with different characteristics to those currently at his disposal.
A deal had been agreed to sign Russia star Aleksandr Golovin from CSKA Moscow, only for Monaco to swoop in and complete a €30m (£27m/$34.8m) move .
Kovacic's arrival will likely see him play alongside N'Golo Kante and fellow new signing Jorginho in Chelsea's midfield, though the Croatia international may need some time to get match fit having only just returned to training this week following the World Cup.
He is set to join Athletic Club goalkeeper Kepa Arrizabalaga in swapping La Liga for west London after the Basque outfit confirmed on Tuesday that the player's £71m ($93m) release clause had been activated .
He is set to replace Thibaut Courtois, whose £31m ($40m) move to Real Madrid should be announced by Thursday at the latest.
Bakayoko, meanwhile, could be followed out the exit door by defender Kurt Zouma after Everton turned their attention towards signing the centre-back ahead of the transfer window closing.