Nabil Fekir and Christian Pulisic are also being scouted ahead of what could be a busy January transfer window for the Blues.
Liverpool agreed a fee worth up to £52.75million for Fekir back in the summer but the deal did not materialise.
It is believed that Fekir's contract in France expires in 2020, and that he has no plans to extend his stay in Ligue 1.
All inside photos, videos from Priyanka Chopra- Nick Jonas reception
Soon after guests started arriving at the venue the bride and groom made a stunning appearance and sent the paparazzi in a tizzy. It wasn't too far from here that I took Madhu (Priyanka's mother) out for lunch to ask if I can marry her daughter.
The addition of Fekir makes a whole lot of sense for Chelsea, mostly from a tactical perspective as it will allow to Sarri to be more flexible and have more options in the attacking department, at least till the end of the campaign.
Sarri's side are now fourth in the Premier League with 37 points from 18 games.
Madrid are studying the possibility of making a move for Fekir, as they are on the hunt for an offensive midfielder who could play a similar role to Luka Modric in the future.