The Chilean winger made the move to Old Trafford in January 2018 - as Henrikh Mkhitaryan went the other way - but after just five goals in 45 appearances in all competitions while on a £505,000-a-week deal, he was loaned to Inter Milan.
Now, the 31-year-old star told Pelotoros TV: "After the first training session I had at Manchester United I realised many things.
"And when I got back home I told my agent if I could cancel the contract and go back to Arsenal."
This summer, Sanchez made his Inter move a permanent one, but he has still only managed five goals in 30 games after previously scoring 80 in 166 for Arsenal.
After agreeing to stay in Italy, the player - who is thought to have received a £9 million payoff to get his huge wages off the books at United - said: "I'm really happy to be staying here with you, Inter fans. I've found a family here and the staff are great.
"It's a group where there's a real desire to win something big.
"People here want to fight together as a team to give the club the success it deserves."