Martial's agent revealed last week that the France international, who has spent the past six years at United, is eager to leave in January due to a lack of playing time this season.
Former Monaco forward Martial has played just 358 minutes of football for the Red Devils in all competitions this season – the 20th most in the squad – and only started four times.
He scored 17 goals under Ole Gunnar Solskjaer two seasons ago, but found the net just four times in all competitions last season and only once so far this term.
But Saha does not believe it is too late for Martial – who has not featured in a matchday squad in Rangnick's three games in charge – to get his career back on track at United.
"He needs a big switch in his mentality," Saha said of his compatriot. "I heard that he doesn't listen to any critics, he just protects himself and his self-belief and all that.
"Sometimes you must listen. You need to hear the critics and understand you have so much potential and that's why you've been criticised – because you can do much more.
"The mentality that Cristiano is showing, that's something that you need to have as a number nine. And the number nine at the moment is Martial.
"So he really needs to be very aggressive. And this is what I want because I think he's a terrific player and it's not because he's French.
"I love his potential when he's playing with full confidence, it's just unstoppable. I can see him being part of this squad when there's a proper aggressiveness in his approach to games.
"Maybe you can last four or five games, 70 minutes because you can't do anymore, but then you go to 80 minutes and then 90 minutes."
Martial is not the only Frenchman facing an uncertain future at Old Trafford, with midfielder Pogba now into the final six months of his contract.
Rangnick stated last week it is not his job to persuade Pogba, who is out until 2022 with a thigh injury sustained last month, to sign a new deal.
Despite featuring in just 13 of United's 22 games in all competitions this term, Pogba's tally of seven assists is bettered only by Bruno Fernandes (eight) among his team-mates.
Indeed, each of those assists have come in the Premier League from nine appearances.
Of those to have played as many games in Europe's top five leagues this term, only Angers midfielder Mathias Pereira Lage (1.08) and Cologne's Louis Schaub (1.24) have assisted more goals per 90 minutes than Pogba (1).
Saha insists there is a place in the United side for Pogba once he has recovered from injury, even if his playing style is not necessarily suited to a Rangnick-coached team.
"It's not like every player needs to press," said Saha, who spent four years at United before leaving in 2008. "That's not the way football is.
"Some players have a great quality to do that and some can read the games and can be the counter-attacker in some way. There are so many combinations.
"This is where the balance is really important for a manager. You need to find the kind of right formula for the players to express themselves to the best.
"Paul Pogba is not well known and you will never be well known to press and be like N'Golo Kante. It's just not his quality. His quality is somewhere else."
Pogba often comes in for criticism, but Saha has urged his countryman to do his talking where it matters most.
"That's the problem for Paul. It's not about quality and it's not about mentality. When he is on the field, he never hides, he works, he commits," Saha said.
"Just play, just enjoy, just work hard, just speak on the field. I don't want to hear anyone talk and I know that.
"And you can see the best players like [Lionel] Messi, Ronaldo, they don't need to speak. Nobody is speaking. You don't need to defend yourself when you're performing."