The 33-year-old has been the Blaugrana's first-choice left-back for nearly a decade after rejoining from Valencia in 2012 but is now facing competition from the up-and-coming Alex Balde.
Alba was given the nod for Barca's opening La Liga draw with Rayo Vallecano, but the Spain international was then dropped to the bench for the 4-1 win at Real Sociedad on August 21.
Eighteen-year-old Balde was selected to start for the second La Liga game in a row as Barca ran out 4-0 winners over Real Valladolid on Sunday, during which Alba was an unused substitute.
Alba will turn 34 in March and also has just two years left to run on his Barcelona deal, which has unsurprisingly led to speculation surrounding his next career move.
Furthermore, Barcelona have been on the hunt for left-back reinforcements the entire summer and are determined to wrap up a deal for Chelsea's Marcos Alonso before the deadline.
With Alonso's possible arrival pushing Alba further down the pecking order, Marca reports that the veteran defender will move to Inter Milan on a season-long loan deal.
The report claims that Barca and Inter have shaken hands on the terms of the deal, but Alba himself has not agreed to the move and is instead keen to continue at Barcelona.
The former La Masia youngster - who initially left Barcelona in 2005 - supposedly feels that by staying at Barcelona, he will maximize his chances of being selected for Luis Enrique's Spain squad for the 2022 World Cup.
However, Barcelona are instead considering his future after a perceived drop in form and alleged problems regarding a pay cut to help the cash-strapped Catalans through the COVID-19 crisis.
Alba has made a total of 431 senior appearances for Barcelona over the past 10 years, scoring 25 goals and setting up a further 94 across all tournaments.
The 85-cap Spain international has collected five La Liga titles, five Copa del Reys, three Supercopa de Espanas, one Champions League and one Club World Cup with La Blaugrana, as well as winning Euro 2012 with Spain.
Barcelona have already cut Oscar Mingueza, Dani Alves and Moussa Wague from their defensive ranks this summer, as well as allowing Clement Lenglet and Samuel Umtiti to leave on loan.
Sergino Dest - an alleged target of Manchester United - could be the next name out of the Blaugrana exit door, as AC Milan are understood to have won the race for his signature.
The USA international has fallen behind Jules Kounde and Sergi Roberto in the right-back pecking order and will arrive at San Siro on loan with an option to buy.