The Belgian is still under contract with Spurs until the summer of 2019, and the Lilywhites have the option of extending his deal for another year.
According to the Times, though, the 29-year-old is unhappy with his current salary in north London, and could be sold in the summer.
Alderweireld in considered to be one of the finest centre-backs in world football, but with Jan Vertonghen, Davinson Sanchez and Eric Dier currently at Tottenham, it could be argued that they can afford to sanction his exit this summer.
Diario Gol claim that Coutinho, who played against the Spurs man numerous times during his spell with Liverpool, has recommended the Belgium international to the Barca hierarchy.
The centre-back is valued at £31.2 million, according to Transfer Markt, but Tottenham would surely demand more than that, if they do agree to sell him this summer, considering the currently inflated state of the transfer market.