The Spaniard is thought to be exploring his options after struggling for regular game time under Luis Enrique.
Despite Lionel Messi being a huge fan of the left-back, Enrique left him out of the starting XI for Barcelona’s 3-0 defeat to Juventus in the Champions League on Tuesday night.
Messi has reportedly told Barcelona’s board to reject any offers they receive for Alba and he is hopeful his team-mate will stay at the end of the season.
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But Spanish publication Don Balon claim he is set to go against the Argentine’s wishes and is preparing to leave.
They say he has already made enquiries to Chelsea and Manchester United about the possibility of a transfer.
The Manchester Evening News revealed last month that Jose Mourinho was chasing Alba’s signature as he looks to bolster his defensive options.
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Meanwhile, Antonio Conte is also keen to improve his defence as he looks to provide competition for Marcos Alonso.
A transfer away from the Nou Camp would be a big blow to Messi, Luis Suarez and Neymar with Alba contributing four assists in La Liga this term.
Alba has been at Barcelona since 2012 and is currently under contract with the La Liga giants until 2020.