Alba, who made 46 competitive appearances for La Liga giants Barcelona last season, is said to be available for around €60m due to a release clause in his contract, prompting interest from various Premier League clubs, including Chelsea and Manchester United.
According to AS, the 29-year-old's contract is set to expire in 2020 and promises of a new contract were made to Alba's agent, Vincente Flores.
However, since Barcelona's Director of Football Raul Sanllehi left for Arsenal in November last year, no contract offer has been made and the player is subsequently keeping his options open, drawing further interest from Tottenham Hotspur.
Jordi Alba is regarded as one of the bets full-backs in the world, having played for Barcelona for that last 6 years, in which time he has won 4 Spanish La Liga titles and has won 1 European Championship with Spain, scoring in the final.
He is known for both his speed and attacking abilities from defence, making him an exciting signing should he move to a Premier League side.
How quickly Tottenham make a move for the player depends on how well Spain perform in this World Cup, as no transfer will take place whilst Alba is in Russia.
Though Alba's focus may be on the World Cup, Spurs are said to have their eyes on a number of talented individuals, having already been linked with Aston Villa's Jack Grealish and Lyon's Tanguy Ndombele.