Kane left Tottenham in a £100 million ($124m) move and will come up against United in the Champions League at the Allianz Arena on Wednesday.
United never got as far as bidding for the England captain -- despite interest from manager Erik ten Hag -- and instead signed Denmark striker Rasmus Højlund but Kane has confirmed there was other interest alongside that of the German champions.
"Obviously over the summer I know there were some talks between a few clubs in the background, but Bayern was a team I was really interested by and really excited by, so there weren't many other discussions," Kane told a news conference in Munich on Tuesday.
"Once they came in, it was between them and Tottenham to talk, and the deal got done. My focus is on here, obviously Manchester United are a great club, a really big club as well, but I decided to come here and I'm really happy I have."
Kane was keen to play against friend and England teammate Harry Maguire but the defender was ruled out of the upcoming tie with an injury.
Maguire has come under more scrutiny following his own goal for England against Scotland during the international break.
"I've come up against friends or England teammates before," Kane added. "Once you get on to the pitch, your competitiveness comes out and you want to do your best for your team and nothing else really enters your mind.
"I think 'H' has come under some really unnecessary scrutiny. Probably been scapegoated a little bit in terms of the way the team has gone over recent times. He is a really good friend of mine, he's a great guy, a really hard working professional."
United head into the game in Munich on the back of a run of three defeats in their past four games. The 3-1 defeat to Brighton on Saturday made it their worst start to a Premier League season and Bayern manager Thomas Tuchel said he feels sorry for the pressure being put on United boss Ten Hag.
"I felt with Manchester United there was always a lot of noise, a lot of pundits are ex-players from Manchester United and you have this legacy from Sir Alex Ferguson which creates a lot of pressure, a lot of expectation around Manchester United," Tuchel said.
"It tells you you work at a big club, big expectation, big success. All of us here in Bayern and my colleague at Manchester United want to achieve the same things.
"I would not say [United's poor form] is an advantage for us. It's common that little things become bigger than at other clubs. I think within, I can only assume they coach an environment where players grow and reach their top level.
"That's what we're trying to do -- instill rules and a winning culture. The results maybe doesn't speak the same language but the team is full of quality and the club has a winning culture. We will never underestimate that."