The Spaniard still has a year to run on his contract at Stamford Bridge, but could be allowed to leave as Thomas Tuchel overhauls his squad.
According to the Mirror, Barcelona are leading the race to sign Alonso amid interest from several clubs in both Spain and England. Barca are pushing forward with negotiations after 'receiving encouragement' from Alonso's representatives about his desire to move to the Nou Camp.
It is stated that driving Alonso's push to join the Catalan giants is the legacy of his father, Marcos Alonso Pena. Pena spent five years at Barcelona and is described as being an 'idol' at the La Liga club.
The chance to follow in his footsteps is said to be a 'major appeal' to the Chelsea star, despite him being tied to the London club for another season. But with Barca interested, Alonso has now informed the Blues of his 'desire to leave' paving the way for the Catalan side to firm up their interest.