The former Red Devils winger says Depay has looked 'fed up' at times, while Martial needs to be offered greater freedom in which to express himself.
The 2015 summer transfer window was another costly one for Manchester United, with the Red Devils splashing out more than £100 million on an array of international talent.
Most of those drafted in have made a positive impression, but some have been unable to maintain the high standards they set shortly after arriving in new surroundings.
Memphis Depay, a player Louis van Gaal knows well from his time in charge of the Netherlands national team, looked lively early on as he opened his goalscoring account in Champions League qualification.
Anthony Martial, another bright young thing expected to deliver an immediate return on sizeable investment, also burst out of the blocks, with an eye-catching individual effort on debut against Liverpool sparking a three-match scoring run.
He has, however, gone off the boil of late, while Depay has faded out of contention completely.
There is little doubt that both possess the potential to be fine additions for United, but Van Gaal needs a find a way of keeping both happy and of bringing the best out of them.
That is a view shared by former United winger Lee Sharpe, who has spotted concerning signs of late which suggest that Depay – along with a few of his teammates – have lost interest in a brand of football which is winning few admirers.
Sharpe, speaking exclusively to 888sport.com ahead of Manchester United’s tie with West Ham United, said: "He came in on fire, full of energy and enthusiasm. It seems to have dwindled a bit and I’m not sure if that’s down to the manager because with Martial we witnessed the same.
“There’s been a few players who have done good little bits but then been left out of the team. They have to start passing sideways and backwards rather than taking risks. He does look a bit fed up, but then again a few others are as well."
Offering his players greater freedom in which to express themselves appears to be the order of the day for Van Gaal, with United having struggled for goals in recent weeks as they endeavour to pass opponents into submission.
Sharpe believes that by breaking the shackles, the likes of Martial – a teenage forward trying to justify a £36 million price tag – will start to show their true colours.
He added: "If he’s there long enough and the manager takes the shackles off him he’ll do alright. You can see glimpses of brilliance. He’s powerful and quick and cool under pressure. All the signs are there that he has the potential to be a great."
You can read the full and frank interview – including Sharpe's thoughts on United’s form, the team under Van Gaal and the form of Wayne Rooney - here, with it clear that the Red Devils require a spark from somewhere.
The fact that they have managed to keep themselves in Premier League title contention, just a point off the pace despite being well short of their best, bodes well, but they must ensure that energy and enthusiasm is maintained if they to sustain a challenge for a first top-flight crown in the post-Sir Alex Ferguson era.