Sanchez arrived at United in January 2018 but left on loan to Inter Milan this summer after a difficult spell at Old Trafford.
"Sanchez…I felt him [to be] not a happy man. And I think in every job you have when you are not happy it is not so easy to perform at every level. And maybe I am wrong. Maybe it was me who was not capable to get into him and to get the best out of him.
"As a manager sometimes you have the capacity to get the best out of the players and other times you are not successful in that approach. But the reality is that I always felt [of Sanchez], 'a sad man.' So probably in Italy he will recover this. I hope he can. I always wish well to every player."
The 30-year-old spoke of his desire to be happy after joining Inter:
After a strong three-year spell with Barcelona in which he won La Liga and the Copa del Rey, Sanchez took his game to new heights upon joining Arsenal in 2014, plundering 80 goals and 45 assists in 166 appearances.
He has declined significantly in recent years, though, as his goal tallies have demonstrated:
In 18 months with United, he made 45 appearances, scoring just five goals, of which three came in the Premier League.
The Chilean's record with the Red Devils has been the subject of some unfavourable comparisons of late, including these from football writers Richard Jolly and Sam Pilger:
Sanchez has perhaps suffered some burnout after playing international tournaments with Chile every summer from 2014 to 2017, giving him little time to recover between domestic seasons.
A return to Italy, where he played with Udinese prior to joining Barca, could help him revive his career with a fresh start at Inter Milan, where it will fall on manager Antonio Conte to get the best out of him.