The Spain international has again been an important player for the Blues during the 2021-22 campaign, making 46 appearances in all competitions, contributing five goals and six assists in the process.
Alonso's contract at Stamford Bridge is due to expire next June, though, and there has been a host of speculation surrounding his future in recent months.
According to Italian journalist Fabrizio Romano, the 31-year-old wants to return to Spain this summer, and the defender has already agreed personal terms with Barcelona.
Romano claims that the Catalan outfit are attempting to negotiate a transfer fee with Chelsea, but the club are not prepared to pay a large amount for his services.
Alonso scored four goals and registered five assists in 28 Premier League appearances during the 2021-22 campaign, in addition to featuring on eight occasions in the Champions League.
The Spaniard also turned out in the EFL Cup, FA Cup, UEFA Super Cup and Club World Cup during a busy campaign, playing a lot of football due to Ben Chilwell's serious knee injury.
Since arriving at Stamford Bridge from Fiorentina in August 2016, Alonso has featured on 212 occasions for the London giants in all competitions, contributing 29 goals and 23 assists in the process.
The left-back started his professional career at Real Madrid but only made one first-team appearance for the Whites before joining Bolton Wanderers in 2010.
A successful period at Fiorentina led to Chelsea bringing him back to the Premier League, and he has won the Premier League, FA Cup, Champions League and Europa League during his time at the club.
Barcelona are believed to be determined to sign a new left-back this summer to provide competition for Jordi Alba during the 2022-23 campaign.
Celta Vigo's Javi Galan, Real Betis' Alex Moreno, Tottenham Hotspur's Sergio Reguilon and Valencia's Jose Gaya have also been linked with moves to Camp Nou to fill the role.
However, Alonso is believed to be the most realistic option for Barcelona, providing that Chelsea allow him to leave for a small transfer fee, 12 months before the end of his contract.
The La Liga giants have also allegedly been in touch with Napoli to discuss a possible deal for Kalidou Koulibaly during this summer's transfer window.
Barcelona, meanwhile, are said to be making progress in their pursuit of Bayern Munich forward Robert Lewandowski, who is allegedly determined to secure a move to Camp Nou in the upcoming market.