Sanchez joined United from Arsenal in January 2018, following in the footsteps of Van Persie who left the Emirates for Old Trafford in 2012.
Van Persie won the Premier League title in his debut season at United, scoring 26 goals to win back-to-back Golden Boot awards.
However, Sanchez has failed to emulate the Dutchman's seamless transition from London to Manchester.
The Chilean is United’s highest earner despite having scored just five goals in 45 appearances in all competitions and is yet to play a single minute this season.
Both parties are now seemingly minded to draw a line under the episode, with Inter Milan poised to provide the desired escape route.
The 30-year-old's decline from one of the league's most coveted players to cast-off has been as sharp as it has been unexpected.
Debate has raged across the media over the potential reasons and causes involved. Van Persie has his own explanation.
“Sanchez doesn’t look happy to me,” he said in an exclusive interview with BTSport.com.
“I can’t properly judge it because I am not working with him but when I see him play I rarely see him smiling.
“Of course, I get it: when you are playing you need to be serious and you want to win.
"But after you score a goal you can smile, because that is the point of football.
“We all play football because we like it and if you like something you should smile.
“I think in the first couple of months after his move he was happy and he was playing well.
“Mentally he needs to find that happiness again because if you are happy then you are fitter, you want to create and you want to have fun."
Salvation for Sanchez could come in the form of a loan move to Inter ahead of the transfer deadline for European clubs on 2 September.
That would see him link up with former United striker Romelu Lukaku, who was also moved on by manager Ole Gunnar Solskjaer after being deemed surplus to requirements.
Van Persie is not ready to rule out Sanchez rediscovering his mojo at the San Siro but admits the Chilean - like Lukaku - may be a victim of the unique pressure that comes with being a Manchester United striker.
“I don’t know if it’s the pressure," said Van Persie, who scored 144 Premier League goals during an 11-year stay in England.
"Pressure is something you can’t see or touch but he has to manage that in his head.
“He is still the same great player. He has it all: he’s fast, he can assist, he can dribble, and he can score.
“There is just a lot of negativity around him from fans and people who have opinions on social media.
“Maybe it’s all become a little too much for him.
"He just needs to block it out, find his true happiness and just enjoy football.”
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