The Bundesliga giants ended a drawn-out saga by completing the signing of Kane for an initial £86million fee in August.
United had reportedly approached Tottenham Hotspur about luring the 30-year-old to Old Trafford earlier in the summer after Ten Hag made him his priority target.
But Ten Hag faced resistance from Daniel Levy before moving onto alternatives, instead signing Atalanta striker Rasmus Hojlund for £72m.
Kane faced the media alongside Bayern boss Thomas Tuchel ahead of the Champions League Group A curtain-raiser.
And England’s all-time top goalscorer was unsurprisingly questioned about other interest in his signature, including from United.
“Over the summer, I know there were talks between a few clubs in the background, but Bayern was a team I was really interested in and excited by,” Kane responded.
“There weren’t many other discussions when they came in, and the deal got done. My focus is on here. Manchester United are a great club and a big club, too, but I decided to come here, and I’m glad I did.”
Kane’s comments follow reports on Tuesday claiming the Spurs legend had his heart set on a blockbuster switch to United.
According to the Mail, Kane was willing to wait until his Tottenham contract expired this summer to join United as a free agent.
He was ready to run down his deal in north London if he received a guarantee that a transfer to Old Trafford would go ahead.
But that never arrived as United turned their focus toward Hojlund, and Kane joined Bayern one week after the 20-year-old Dane landed in M16.
Many had doubts over Kane’s desire to move overseas as he chased down Alan Shearer’s all-time Premier League goal record.
The iconic Spurs No 10 left British shores in second with a tally of 213, possibly two seasons-worth of strikes behind Alan Shearer’s 260.
It has left some expectation that Kane will return to the Premier League once he has tasted silverware with Bayern, potentially in the form of the Champions League.
But he has played down that prospect, adding: “I don’t think it was something I was thinking about [the record]. There was a lot of noise about it, but those individual records have never been a focus of mine.
“Ultimately, for me it was about how I can push myself, get better, and challenging for titles every year is how I give myself that opportunity.”
