Dybala has been compared with the five-time Ballon d'Or winner as his profile continues to grow at Italian champions Juve.
The 23-year-old Argentine forward has netted 14 goals in all competitions this season but insists he is his own man amid claims of similarities with one of the world's greatest.
"People have to know that I'm not Messi. I am Dybala and I want to be only Dybala, although I understand that there are comparisons," Dybala told Marca.
"Messi, there is only one, as there was only one Maradona.
"You cannot replace players like them. It is a burden that people have expectations about me.
"I will try to compensate them by giving the maximum."
Dybala has been linked with a move to Barca, who are reported to have the former Palermo striker on their radar as they consider their transfer options.
He is yet to sign a new deal but remains contracted to Juventus until 2020.
"Three years ago, in Palermo, I did not think I would go to Juve," Dybala said. "Therefore, I enjoy day-to-day and I do not think beyond.
"I am happy here, where everyone loves me very much. I feel at one of my best moments."