Last summer, the Blues paid £23m to sign the left-sided player from Fiorentina, and he has gone to be play a leading role in Chelsea's Premier League title success.
The Spaniard has contributed six goals and three assists from left wing-back, but it appears that his form has attracted attention back in his homeland.
According to Mundo Deportivo, Barcelona are looking to strengthen their squad with a versatile left-footed player and 26-year-old Alonso fits the bill.
Chelsea will have no desire to sell a player who has proven invaluable since their switch to a 3-4-3 formation, but it has been claimed that the Catalan giants are ready to make a significant effort to try to take the player to Camp Nou.
Alonso started his career at Real Madrid but he only made one substitute appearance for Barcelona's great rivals, which came as a 90th-minute replacement in April 2010.