Even with just a single year remaining on his Borussia Dortmund contract the Armenia international moved to Old Trafford for a reported sum of £26.3million.
"... it doesn't matter if they buy me for, I don't know, €38m or €40m, I am not guaranteed to play the games, so I am trying to do my best during the training to earn this place to play and then we will see," said Mkhitaryan.
"I don't think I will play every game, depending on the tactical situation, depending on the opponent, but I will do everything to try and help the team."
Mkhitaryan is also mindful that former Dortmund team-mate Shinji Kagawa left the Signal Iduna Park in 2014 and failed to make an impact at United.
"In this club, you have to try and do everything to show your best qualities, otherwise you will not be here anymore," he said with regard to the Japan international.
"So I will try to do my best, I will try to help the team win the games, try to keep fit and bring my sharpness to the team.
"I never promise something, I always say that I will try, because if you promise something and you don't do [it] you will always be under pressure.
"So that is why I'm trying to say I will do all my best and I will try to help Manchester because, for me, this is a new challenge and I like difficulties.
"I like to [overcome] the difficulties because when you win [despite] the difficulties it makes you stronger, so I'm trying to do everything to come up to a new level."