The 42-year-old, who is set to replace Pep Guardiola in the summer, wants to bolster the Catalans' rear guard, and has made the left-back his top priority
The Spain international, who has been one of Los Che's top performers this season, was in Barca's youth system for seven years before leaving in 2005.
Barcelona currently do not have a natural left-back at their disposal, following the sale of Maxwell in January and the uncertainty over Eric Abidal's future after his liver transplant earlier this month.
Alba is believed to be the Catalans' preferred choice due to his familiarity with the club, and it is rumoured that the player has already agreed to a move, with only details over the transfer fee to be ironed out.
Barcelona are reportedly willing to acquire him this summer, rather than waiting to take him on a free transfer when his contract runs out in 2013.
The Blaugrana are set to face fierce competition for the player's signature, however, as Manchester United, AC Milan and Napoli are also believed to be eyeing up a move for the left-back.