The aformentioned source claims that Pochettino is keen on adding a new anchor man to his side this summer and will use the World Cup to run the rule over the Colombian international.
The 24-year-old currently plies his trade in Argentina with Boca, having joined them from Deportes Tolima in his homeland two years ago.
Barrios is a tough-tackling midfielder and would add some bite to the Spurs side, where he could team up with compatriot Davinson Sanchez.
According to 'The Sun', Spurs are considering a move in the region of £25m for the player, who has 10 caps for his country.
Space in the squad could be generate by moving on Victor Wanyama, who has struggled with injuries of late.