Martial is just 19 years old but Man United were willing to part with £36m to complete a move for him on deadline day.
Pogba was at United as a youngster himself but he eventually left for Juventus after falling out with Sir Alex Ferguson.
The Frenchman believes his compatriot will flourish in the Premier League before kicking on for the national side.
“I call him [Martial] ‘the young old man’ because he’s 19 and he’s already so mature for his age,” Pogba said.
“I already knew him well, he has great ability and a huge amount of potential. He will bring a lot to the French team. I’m very happy for him, he’s changed clubs now, he’s in the Premier League where he will train with great players and will keep improving.”
Martial has huge pressure on his shoulders but a number of his French teammates have been talking up his ability. Along with the likes of Luke Shaw and Memphis Depay, United have a promising group of youngsters who should provide the platform for the team to build on in the coming years.