Alba, 23, has emerged as a key target for both clubs this summer after establishing himself as one of the game's top full-backs with his dazzling displays for Valencia last season.
Barca have been on the trail of the marauding full-back, a graduate from the club's famed La Masia academy for much of the season, as doubts persist over the long-term future of Eric Abidal in the game following his liver transplant.
Meanwhile, United boss Sir Alex Ferguson has had Alba, tipped to star for Spain at Euro 2012, watched on a number of occasions this season as he begins the search for a long-term replacement for Patrice Evra, who turns 31 later this year.
However, reports in Spain suggest Barca are favourites to land their former star, who left the club in 2005, with respected journalist Guillem Balague claiming the player has already agreed terms at the Camp Nou.
"Jordi Alba has got an agreement with Barcelona, but FCB needs to reach a deal with Valencia (his deal finishes in 2013)," Balague tweeted earlier today.
Valencia are bracing themselves for a bid as Barca's new boss Tito Vilanova sets about reshaping the squad he inherited from Pep Guardiola.
"I suppose Barcelona want him because he’s Catalan and plays on the left wing," said Valencia's sporting director Braulio Vazquez. "We are obviously talking about an excellent player, and it’s only normal that Barcelona are keen to sign him."