Suarez is no stranger to the Premier League, having spent two seasons with Manchester City earlier in his career.
The classy playmaker joined City from Celta Vigo in 2011, before making the move to Barcelona two years later. A move to Villarreal followed, where his impressive performances convinced the Catalans to bring him back to the Camp Nou just a year later.
Milan have long since been mooted as a potential suitor, but with the Italians looking to sign him on an initial six-month loan with a view ot a permanent deal, Chelsea are hoping to steal a march on their rivals by offering a cash deal next month.
The 24-year-old is keen for a fresh start in the New Year having so far failed to force his way into Ernesto Valverde's plans, making just two appearances so far this season.
Maurizio Sarri is said to be a huge fan of the Spain international and is hopeful of adding him to his ranks come the turn of the year.
The Italian's impressive start to life at Stamford Bridge is expected to see him backed to the hilt in the transfer market by owner Roman Abramovich, meaning Suarez could be the first of a host of new recruits.