Leicester are set to ask Chelsea for the money they received following the sale of Nemanja Matic to Manchester United if they want to sign Danny Drinkwater.
The Telegraph have reported that the Premier League champions will make a £25m bid for the midfielder having already had a £15m offer rejected.
But Leicester are reportedly set to hold out for their asking price of £40m, the same fee United paid Chelsea for Matic.
Antonio Conte is looking to strenghten his squad before the end of the transfer window having grown increasingly frustrated by the club's lack of depth.
After Saturday's shock 3-2 loss against Burnley at Stamford Bridge, Conte has reportedly been promised that three new signings will be made before the end of the month.
With Cesc Fabregas' sending off in the defeat and the absence of new arrival Tiémoué Bakayoko through injury, the Blues now have a dearth of options in midfield.
But there are concerns that Leicester could prove difficult to negotiate with over the potential transfer of Drinkwater.
The 27-year-old is two years younger than Matic and his status as a homegrown player would be useful for Chelsea who are competing in both the Premier League and Champions League this season.
Drinkwater, who has four years remaining on his contract at the King Power Stadium, was left out of Leicester's team for the opening day 4-3 defeat against Arsenal at the Emirates on Friday.
A move to Chelsea could see the England international reunited with former teammate N'Golo Kante.