Martial, 21, joined United from Ligue 1 champions Monaco two seasons ago in a deal that could rise to £58m, (€64.2m, $75.4m) but failed to establish himself as a part of Jose Mourinho's starting line-up after impressing under Louis van Gaal.
Arsenal were reported to be considering a £40m bid for Martial this summer, while Inter Milan were interested in a swap deal involving him and Ivan Perisic, who has been courted by United for a number of months.
Arsene Wenger is a known admirer of Martial, who was left on the substitutes' bench as United lost 2-1 to Real Madrid in the UEFA Super Cup on Tuesday (8 August), but Arsenal's interest in the France international seems to have dulled with the Gunners now pursuing Monaco's Thomas Lemar. A move to Inter Milan also looks rather unlikely at this stage, with United reluctant to sanction a loan deal for the lauded 21-year-old.
Jose Mourinho insisted that Martial is part of his plans earlier this summer but Parker, who plied his trade at Old Trafford between 1991 and 1996, thinks a move might be in the former Monaco wonderkid's best interests.
The former United defender believes Martial currently plays for the "best club he can be at" but says he needs a change of scenery in order to enjoy his football again. There was an incredible amount of hype surrounding Martial when he arrived at Old Trafford in the summer of 2015, but Parker does not think the versatile forward is doing enough to suggest that he will fulfill his vast potential.
"When you look at him as a player he really doesn't look like he's enjoying himself," Parker said, speaking exclusively to 888sport. "If anyone could tell me that they've seen him smile on a pitch then I'd say they must have a 200 inch television that's picked up the slightest flicker at the side of his mouth. You don't see him play with any smile on his face. There is nothing in him and he's not relishing the challenge. He's not doing enough and isn't proactive, he reacts.
"You need that little bit more because he came to Manchester United with the same hype as Kylian Mbappe. He was a wonderkid, he was French, he was black, so suddenly he was the next Thierry Henry. I really don't see him getting an advert for Clio at this moment in time.
"He needs a change, to get a smile on his face and enjoy his job. He's a young boy at the best club he can be at but he's not enjoying it and Manchester United is not a nice place when you're under pressure and not playing all the time."
Despite Parker's calls for Martial to leave United, a move to Arsenal, Inter or indeed any club looks unlikely at present. The former Lyon academy product may well have designs on a move away from Manchester in the coming weeks, but for now he will be hoping to force his way into Mourinho's starting line-up for United's Premier League opener against West Ham United.
Read the full 888sport interview with Paul Parker, including his thoughts on why Mourinho has to deliver this season.