Adebayor revealed to The Sun: "When I got that approach from United, I was like 'OK, it's a good team, one of the biggest teams in the world - why not?'
"But don't forget I am already at a massive club and we have a fantastic team.
"I had a good discussion with the boss Arsene Wenger, we finally sorted everything out and I was very happy."
United had contacted Adebayor's agent Stephane Courbis to declare their interest midway through last season.
He added: "I don't know if what prompted United's interest was my winner at Old Trafford. But I hope to do that again on Saturday.
"I did the right thing in signing a new deal with Arsenal - a four-year contract.
"I am just like a baby boy who was born in this club.
"It's a family team, everyone loves me - and the fans, the players, the boss . . . we are all like brothers."