Lewandowski was favourite to take home to award. However, it was cancelled in June by organisers who said the impact of the coronavirus pandemic on football made it unfair to go ahead with the judging.
The 32-year-old was asked by reporters who deserved to win the 2020 Ballon d'Or and he replied: "Me."
The striker finished as top scorer in the Bundesliga, the German Cup and the Champions League, racking up a total of 55 goals in the 2019-20 season and was instrumental for his club as they won their second continental treble in only seven years.
"We won everything we could with Bayern," he added. "I was the top scorer in all competitions I featured in and I think a player who achieves this would win the Ballon d'Or."
The 32-year-old has spent the past decade chasing his dream of winning the Champions League.
He came close in 2012-13 when his previous club Borussia Dortmund lost the all-German final against Bayern but has not reached the final of the competition since, missing crucial matches in the latter stages through injuries.
When the final whistle blew against Paris Saint-Germain, Lewandowski was visibly emotional as he sunk to the ground in celebration.
"Until now, I was hiding emotions behind a thick shell, but the Champions League is every footballer's dream and I've believed all my life that I could fulfil it," he said.
"I was close many times, but something was missing, something was causing us to be knocked out early. Now that we have won it, there was a childlike joy, something natural and spontaneous. I had no control over it."
However, he has said he thinks it was an unfair race to begin with."I find it a shame we play four games less in Bundesliga. It would be a more even competition if everyone had the same number of matches," Lewandowski said.
"If we had 20 teams in Bundesliga just like there are in Italy, Spain, England and France, it would be more objective, that's a difference."
"Manu has been in superb form throughout the 2019-2020 season," Low said.
"Manu is a class of his own. Madness, unbelievable!
"I have nothing against Robert Lewandowski, he is an extraordinary goal getter but for me this year the world's best football would be Manuel Neuer. Just looking at those saves at the mini-tournament in Lisbon."