Having already swooped to sign Andreas Christensen as a free agent from the West London club, Barca are being tipped to bring both Alonso and Cesar Azpilicueta to Camp Nou before the current window closes.
Alonso and Azpilicueta are both out of contract in the summer of 2023, which leaves Thomas Tuchel at risk of seeing more defenders leave on free transfers within the next 12 months.
Left-back Alonso has also confirmed his desire to play in La Liga before he hangs up his boots, telling Onda Cero: "I have one more year of my contract.
"I have already said that I would like it, but in the end it does not depend entirely on me. It is clear that the desire to one day play in Spain is there."
However, should Chelsea successfully keep Alonso on the books at Stamford Bridge this summer, Sport claims that Angelino has been lined up by La Blaugrana as an alternative option.
Barcelona have frequently got one over Chelsea in the current transfer window, firstly beating the Blues to Raphinha's signature before hijacking a move for Jules Kounde from Sevilla.
Tuchel was also thought to have been interested in a reunion with Ousmane Dembele after he became a free agent last month, but Barcelona eventually agreed a new two-year deal with the Frenchman.
As a result, there have been suggestions that Chelsea could block both Alonso and Azpilicueta from moving to Barcelona, forcing the Catalan club to seek out other options as they try to find competition for Jordi Alba.
Former Manchester City prospect Angelino is under contract at the Red Bull Arena until 2025, but Die Roten Bullen are said to be open to his exit after signing David Raum from Hoffenheim.
The report adds that Barcelona have had a long-standing interest in Angelino, but a move for the 25-year-old has never materialised due to Leipzig's previous high asking price.
However, La Blaugrana could now try to secure a loan move for the Spaniard before making his deal permanent in 2023, which would put less immediate strain on their finances.
Angelino is said to be keen to return to his homeland, and Barcelona have already been offered the chance to sign the player, who spent one and a half years on loan at Leipzig before making his move permanent in 2021.
Since 2019, Angelino has registered 12 goals and 28 assists in 98 appearances for Leipzig - often from a wing-back area - and he ended the 2021-22 season with three goals and 13 assists from 45 games in all tournaments.
The former Spain Under-21 international was an unused substitute in May's DFB-Pokal final victory over Freiburg and was not involved in the weekend's DFL-Supercup defeat to Bayern Munich, with manager Domenico Tedesco confirming that his absence was transfer-related.