According to TEAMtalk, the Foxes are interested in taking Drinkwater on loan, with a view to a permanent transfer, although they are only willing to pay £20m to sign the central midfielder on a permanent basis.
Drinkwater is a familiar face to Leicester fans as he was a key member of the club's squad that won the Premier League in the 2015/16 season. He missed just three league games during that famous season.
Chelsea signed the former England international for £35m on deadline day last summer, in a late move that caused one of the dramatic transfer fiascos in recent years. Leicester replaced Drinkwater with Adrien Silva at the very last minute, but failed to register the transfer in time - missing out by just 14 seconds - meaning that Silva could not play for Leicester until January this year.
Leicester may face competition for Drinkwater, though. Southampton, Newcastle and Crystal Palace have all recently been linked with a move to sign the 28-year-old, who has three caps for the England national team.
Meanwhile, Chelsea have reportedly received a shock £100m offer from Real Madrid for duo Thibaut Courtois and Willian. The duo have been heavily linked with a move away from Stamford Bridge this summer, with Los Blancos linked with several potential new Galacticos who could be brought to the club over the summer.