Dressed in black from head to toe, sporting a T-shirt with the white legend “Invader”, and in shy mood at Manchester United’s Carrington training base, Anthony Martial has a welcome message for fans about his affinity for the club and his long-term future.

The 20-year-old is one of Europe’s most sought-after talents and has been linked with a move to Paris Saint-Germain following an impressive first season at United. On Saturday at Wembley against Crystal Palace Martial hopes to fire the club to a 12th FA Cup triumph and a first since 2004, by adding to his 17 goals in 48 appearances.

It was Martial’s superb strike in the dying moments against Everton in the semi-final that sent United into their first Cup final since losing to Chelsea in 2007. The celebration featured the Frenchman jumping into the delirious supporters behind the goal.

Now, asked if he can see himself at United for a long time, despite the interest of PSG, Martial says: “You never know what happens in the future but certainly the fans have accepted me really well and the fact they sing this song about me all the time shows they’re quite happy with me. I just do my best to try to pay back that support.

“I love Manchester and I love being here and certainly I see myself being here for a good while yet. I’m certainly happy here.

“The way the fans have accepted me – I have got a special relationship with them and I’m grateful because they’ve always been there for me. From the moment I arrived they’ve done their best to make me feel relaxed and part of things. It has gone some way to helping me in my overall settling-in period.

“The semi-final goal was very important. It was the one that got us through and killed off the match because it was so near to the end. It was great to go into the crowd and celebrate with the fans and great to get through to the final.”

The chant Martial mentions makes fun of some of the media coverage of last summer’s move from Monaco for £36m, a fee that could rise to £58m. At that moment he was a relative unknown and the ditty goes: “Tony Martial came from France/English press said he had no chance/50 million down the drain/As Tony Martial scores again”.

Does he ever join in? The question brings a first smile. “I don’t really know the words, well at least all of them anyway,” he says.

After the forward signed for United Wayne Rooney had to ask Morgan Schneiderlin, another French player, who the new purchase was. There is a shrug. “Well, he knows me now doesn’t he,” Martial says, laughing. “I’ve heard that story as well. I guess it’s pretty amusing.”

The fans’ adoration was ignited inside the first half-hour of his United career. Liverpool were the opposition at Old Trafford on 12 September when Louis van Gaal took off Juan Mata and brought on Martial after 65 minutes. With United leading 2-1 and Liverpool pressing for an equaliser after Christian Benteke’s goal a few moments earlier, Martial glided along the left, mugged a hapless Martin Srktel twice and beat Simon Mignolet with a cold-eyed 86th-minute finish at the Stretford End that sent the home crowd ballistic.

This is his outstanding moment of the season – so far. “It just couldn’t have been a better way to start,” he says. “From being a young kid I’d dreamed of playing at Old Trafford and to be able to score in my first game in such a way against such an important opponent, United’s biggest rival, it couldn’t have turned out any better.

“It was positive, gave me lots of confidence, it helped me to settle in as a player. Fortunately, things started to go well for me from that moment on and I kept scoring regularly.

“That does create more expectation among the fans but I still consider I’m a player who has a lot to learn and I’m going to carry on learning and progressing as an individual.”

Paul Scholes’s criticism of United’s travails under Van Gaal is usually welcomed by fans, but when the former midfielder claimed in November that Martial was not a centre-forward who “lives for goals” Scholes felt a backlash. Again, in the calm manner that allows such a young man to play with freedom, Martial is unruffled. “I’d heard about that,” he says. “Goalscoring is what I do and it’s the thing that makes me most happy. But I’m not the sort of guy who shows that sort of emotion on the outside too much. But not happy when I score? Scoring makes me happiest because it’s what it’s all about.”

As the song about him and the story involving Rooney illustrates, there was a view Martial’s large transfer fee would prove a staggering waste of money. Now, the opposite appears true. Even if the sum reaches £58m he will be bargain should this season’s form be repeated over the coming years. Martial acknowledges the pressure of the price tag and points to how his previous transfer, to Monaco in June 2013, prepared him.

“What helped me in that situation is I’d already gone through quite an expensive transfer when I moved from Lyon and that created a lot of interest and people spoke about it a lot in France,” he says. “I just tried to remain true to who I am as a person, keep calm and do my best. My first season has gone OK but I’m hoping to have a better season next time around. I didn’t try to put too much pressure on myself. People mention the price tag but I just came here to do my best. Things have gone relatively well but I still feel deep down I could have done better than I have done.”

United have a long tradition of canonising players. These include Eric Cantona and Cristiano Ronaldo and of joining this group Martial says: “You can’t possibly say at this early stage. It all depends on how I play, how many goals I score, how I perform in the years to come. If that was to be the case and I was to become an icon then I’d be very happy.”

There is one match remaining of his first season and by the end a disappointing United campaign that ended with failure to qualify for the Champions League could at least end in FA Cup glory.

“I wasn’t too aware of the history of the competition but I know every trophy you can win has huge importance and we’re going to try to do everything we can to bring the cup back to Manchester,” Martial says.

“It was a fantastic atmosphere [at Wembley against Everton]. It was full for the semi but I guess it’s going to be an even better atmosphere in the final and we’re just going to do everything we can to make sure we win.”