Arsenal were looking to offload the Chilean before his contract ran out.
And United were happy to let Henrikh Mkhitaryan go in the opposite direction.
But Bleacher Report claims that Mourinho was not sure whether the player would fit in the team.
And he also had concerns about signing the player halfway through a season, which he believes can hinder their ability to settle into the team.
Sanchez has endured a difficult spell at United since joining, only managing three league goals.