Under, who joined Roma in 2017, has scored four goals and provided four assists in all competitions this season.
Spurs boss Mauricio Pochettino is looking to bolster his attacking department, having failed to sign a single player in the summer transfer window, and signing a forward is one of his top priorities.
The report claims that Spurs have already seen a bid in the region of £30 million rejected for the 21-year-old. Roma are looking for a fee of around £45 million.
Under is a highly rated young talent and he is often dubbed as the ‘next Paulo Dybala’.
Spurs are choc-a-bloc with attacking talents, but adding Under to the squad would be a smart move.
Arsenal are also equally interested, and the Gunners scouts watched him score a brilliant equaliser in Roma’s 2-2 draw with Inter Milan.