The 18-year-old is reportedly attracting plenty of interest from several clubs, including the Premier League duo.
The 18-year-old is currently out on loan with Serie B side Pescara, and has helped the club make a promising start to the season. The Delfini currently sit sixth in the table, which, if they remained there, would see them qualify for the play-offs.
Mandragora - who is now an Italy U21 international, having made his debut in August - is a holding midfielder, who may be available for £7m (via Evening Standard).
However, the Premier League duo may well have a difficult task on their hands if they wish to convince Mandragora to come to England. The Evening Standard report that Serie A leaders Inter Milan are the current favourites for his signature, after the player described the prospect of playing at the San Siro as "special."
If Mandragora is forced to make a decision between a move to either the Boleyn Ground or Stamford Bridge, it would arguably be more sensible for his career if he was to join Slaven Bilic's men.
Chelsea have over 30 players out on loan (via the Independent), and with Mandragora clearly not ready to keep the likes of Nemanja Matic or Cesc Fabregas out of the side, it would seem inevitable that he would be sent out on a temporary deal.
And while there are a similar number of players in Bilic's squad that are likely to prevent the prospect from holding down a regular spot in the side, the chances given to youngsters like Reece Oxford - who made his debut in the position Mandragora is most comfortable - suggests that he would be given an opportunity much sooner.