Chile international Sanchez is expected to complete a £35m move from the Emirates Stadium to Old Trafford in the January transfer window after the Red Devils swooped in to hijack Manchester City's reported move for the striker.
However, any deal going through is subject to Mkhitaryan agreeing terms with the Gunners, according to the Armenia international's agent Mino Raiola.
"Sanchez is part of Mkhi's deal. Not the other way around. Without him, Sanchez simply cannot go to United," Raiola told Sky Sports News.
He added: "Mkhi's problems at Man United are purely related to playing football. He has no problem with the manager [Jose Mourinho]. It is not personal.
"And he has two and a half years left on his contract. He doesn't have to leave."
When asked to rate the chances of a deal being agreed with Arsenal, Raiola said: "At this moment low, but life is dynamic.
"This is a great deal for Arsenal. They need better, younger players and they have to invest. So it's up to Arsenal to put a deal in place and right now a deal is a long way off."