The 30-year-old forward completed a season-long loan move to Inter Milan this summer following a miserable 19-month spell at Old Trafford, where he managed just five goals in all competitions.
Romelu Lukaku sealed a permanent switch to the San Siro at the start of the month and Sanchez was desperate to follow in the Belgians footsteps in order to improve his first-team prospects and revive his stuttering career.
The Chile international was Uniteds top earner on around £400,000-a-week and Inter have reportedly agreed to pay the majority of these wages until the end of 2019/20 campaign.
Im very happy I went to Manchester United, Sanchez told BBC Sport.
Ive always said that. Its the club thats won the most in England.
When I went to Arsenal it was fantastic – I was happy there – but United were growing at the time, they were buying players to win something.
I wanted to join them and win everything. I dont regret going there.
Sanchez claims he was never given enough game-time to succeed at United after making only nine starts in the Premier League last term.
I think that Im happy when I play for my national team, he said.
I was happy at Manchester United too, but Ive always said to my friends: I want to play.
If they would let me play Ill do my best. Sometimes Id play 60 minutes then I wouldnt play the next game – and I didnt know why.
Solskjaer left Sanchez out of his pre-season plans, but the former Arsenal attacker insists he was ready to play for United.