El Mundo Deportivo says as they seek a new fullback signing this summer, Barca have Alonso on their shopping list.
The 26 year-old is in only his first season with Chelsea, having helped the Londoners to the Premier League title, which was confirmed on Friday with victory over West Brom.
Making a move to Barca difficult will be Alonso’s Real Madrid background, along with Chelsea’s reluctance to sell.
Blues teammate Cesar Azpilicueta has also been linked with Barca for the summer market.