The Frenchman had a stuttered season last time round, starting just 18 Premier League games during the 2016-17 campaign.
Martial failed to make the starting lineup for last weekend's 4-0 win over West Ham United but impressed after coming on with a goal and an assist.
Mourinho, meanwhile, has been vocal in his desire to add a wide player to his squad this summer, but when pressed on the issue, he stressed that this was not a dig at the 21-year-old.
"I have faith in Anthony," Mourinho told reporters during Friday's press conference. "Probably the player I was looking at was not a pure winger because I have pure wingers.
"Probably the player that I was looking for is a player that allows me to play with three at the back and play wing-backs.
"Because - as a pure attacking player - Anthony is a good player. He is one of the players I believe is going to have a better season this season than the previous season.
"I look at some of my players and I am sure that some players are going to be better. Anthony is that for sure."
Tottenham Hotspur have reportedly launched a bid to sign Martial, but United are believed to have rejected the North Londoners' advances.