Dlamini captured attention after being named Player of the Tournament at the recent SAFA/SAB Under-21 Championship in Soshanguve, Tshwane.
The 21-year-old netted nine goals at the competition, which was won by Free State province on Saturday.
"AmaTuks have already met the player's representative and everything looks positive," says a source close to the Secund-born player.
Dlamini's agent Tim Sukazi says other PSL outfits are also interested in his client.
"It's not only AmaTuks but also other PSL teams," says Sukazi.
"I met their football manager [at Tuks] but it will be the survival of the fittest."
Meanwhile, Dlamini says it is dream to compete in the topflight.
"I want to play for a small team first to get more game-time and exposure."