TalkSPORT claims Arsenal and United are tracking the 16-year-old defender, who is yet to feature for the Bundesliga club.
Tah is a Germany under-17 international, and is held in high regard by Hamburg, who view him as a potential first-team regular.
His performances at youth international level have piqued the interest of scouts from abroad, and Manchester United and Arsenal are both reportedly keeping tabs on the youngster's contract situation.
Tah also qualifies for the Ivory Coast, but so far he has chosen to play for Germany at international level. Only when he plays a competitive fixture for the full national team will Tah have to make a decision over his international future.
But at club level he could have a choice to make sooner. Tah is under contract with Hamburg until 2014, but the Premier League pair have an strong record of bringing through talented young players into the first-team.
Danny Welbeck and Tom Cleverley are the most recent graduates from the Manchester United academy, while Arsenal stars Kieran Gibbs, Jack Wilshere and Serge Gnabry are recent additions to the Gunners first-team.