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.
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.
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However, pulling off such a transfer would be hard for Barcelona given the Spaniard is happy at Chelsea after the Premier League side won the league title last night.
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.
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Jordi Alba has been linked with a move away from the club after seeing his game time limited.
Alonso is also slipping off the Spanish radar ahead of the 2018 World Cup, and a move back to Spain could guarantee him a spot on the plane.
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Barcelona looked very light at the back in their Champions League losses to PSG (4-0, which they overturned) and Juventus (3-0, drawing 0-0 at the Camp Nou and going out at the quarter-final stage).