But Manchester City also have eyes on Chilwell, who would compete with Benjamin Mendy at left-back.
Pep Guardiola is looking at returning Oleksandr Zinchenko to his old midfield position, creating a vacancy.
City and Chelsea will have to pay an eye-watering fee for Chilwell if they make their interest official.
According to the Telegraph, Leicester rate Chilwell as highly as Harry Maguire, who was sold to Manchester United for £85m.
City’s strategy is usually to buy players between £60m and £70m, rather than breaking transfer records.
Rodri, a £63.6m signing from Atletico Madrid last summer, is the Manchester club’s record signing.
Chelsea will also be reluctant to spend £85m on Chilwell, which could make transfer talks difficult.
Frank Lampard must also make room in his squad for Chilwell by selling Marcos Alonso or Emerson Palmieri.
Chilwell, who has become England’s first-choice right-back, has made 23 Premier League appearances for the Foxes this season.