Tuttosport says with Juventus keen, the Blues are looking for a fee between £58.1million (€65m) and £62.6m (€70m).
He is under contract until the summer of 2023, which explains the size of the fee.
If Chelsea were to sell Jorginho for their desired price then it would represent a basic profit on the initial £50m fee they handed Napoli two summers ago.
Juventus are on the hunt for a midfielder because Miralem Pjanic is set to be moved on after failing to win over coach Maurizio Sarri.
A swap deal involving Jorginho has been mooted, while the Serie A giants are also hoping to trade Pjanic for Barcelona's Arthur.