Alexis Sanchez filmed kissing Gunners badge in training
Sanchez is out of contract at the end of the upcoming season and has been linked with moves to Manchester City, Bayern Munich and Paris Saint-Germain.
Arsenal boss Arsene Wenger has publicly stated several times his star man would not be leaving, despite the risk of him going on a free next summer.
Mills believe Sanchez wants to quit the Gunners and says having a player with that mindset is not good for a football club.
"I think Arsenal might struggle this season, that is in the caveat that I believe Sanchez will go," Mills said on Sky Sports News.
SKY SPORTS
Alexis Sanchez will leave Arsenal this summer, believes Danny Mills
I think Arsenal might struggle this season, that is in the caveat that I believe Alexis Sanchez will go
Danny Mills on Arsenal star Alexis Sanchez
"He clearly wants to leave, he only wants a year left. Do you keep a really unhappy player?
"Sanchez was pivotal to how sort of successful Arsenal were last season, I know it was their worst season for some time.
"But if you take Sanchez out of that side, they drop down in my opinion to sixth or seventh in the table.
"Even if you keep him with a year to go, he'll be thinking 'I don't want to get injured, am I going to play absolutely full-tilt every game?'.
SKY SPORTS
Arsenal would be wrong to keep an unhappy Alexis Sanchez, says Danny Mills
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"It would be brilliant to say yes, and he should be a professional and he should do that job, but in the real world it doesn't work like that.
"If he just drops by five or 10 per cent, that's a huge margin for Arsenal Football Club.
"You've almost got to bite the bullet and give him what he wants to keep him at Arsenal and get back in the Champions League."
