The two clubs are no strangers to each other when it comes to negotiating deals, officials from both teams currently discussing the future of Romelu Lukaku.
Over the coming days, that saga is expected to reach a conclusion, the likelihood being that the Belgian will make a return to San Siro.
However, according to Italian journalist Gianluca Di Marzio, Chelsea hold an interest in signing one of Inter's top prospects.
Casadei is said to be on the Blues' radar, the 19-year-old being tipped for big things at Inter despite having not made his first-team debut.
Instead, the teenager spent the most recent campaign starring in Primavera 1, contributing 14 goals and four assists from 30 appearances for the Under-19s.
The Italy Under-19 international also racked up seven outings in the UEFA Youth League, Inter making it through to the intermediate stage before losing to MSK Zilina.
Despite Chelsea's interest and Casadei's lack of senior experience, the report claims that I Nerazzurri have no interest in accepting what is described as 'an important proposal'.
In light of admirers emerging from elsewhere, Inter may now attempt to extend Casadei's contract past the end of the 2023-24 season.
While Inter seemingly want to sign Lukaku on a straight loan deal, it has been widely claimed that Chelsea are intent on receiving at least one player in part-exchange.
Casadei could have theoretically being used in that manner, but a report has suggested that Thomas Tuchel would like to sign Milan Skriniar.
The West Londoners require two centre-backs to replace Andreas Christensen and Antonio Rudiger, and Skriniar would fit the profile that Tuchel is searching for in a alternative.
Furthermore, the 27-year-old has just 12 months remaining on his contract, realistically leaving Inter open to offers for one of their key players.
Although Paris Saint-Germain are said to be monitoring the situation, the Ligue 1 champions are allegedly yet to make a breakthrough with regards to a price.