Lautaro is emerging as a priority summer target for Barca, where Messi has recommended his signing to the board.
Agent Beto Yaque told Mundo Deportivo: "Surely for Lauty it is a great compliment from the best in the world. I think that is very nice and comforting for him."
On talk of interest from Barca and Manchester City, Yaque was coy.
He continued: "He wears it as if nothing, because he is only focused on his club but surely with great satisfaction knowing that he is doing things very well for all this.
"For me he has some things from Kun and things from Luis Suárez but in reality he has everything, that's why he is a different player."