The forward was in the middle of his four-year spell at Borussia Dortmund when Red Devils boss Sir Alex Ferguson came forward with an offer.
Lewandowski scoops FIFA’s The Best awardLewandowski scoops FIFA’s The Best award
The Bundesliga side refused to sanction a sale, and Ferguson subsequently turned his attention to signing Robin van Persie from Arsenal, but it is a move the Poland international was interested in.
“After my second year in Dortmund, I had a conversation with Sir Alex Ferguson,” Lewandowski told France Football. “He wanted me to come to Manchester.
“I was very interested. I can even say I was ready. But Dortmund didn’t want to let me go. It didn’t upset me more than that because things were going well with Borussia.”
While he has admitted he was ready for a move to Old Trafford, it could be argued it worked out better by not heading to Manchester.
United won the Premier League title in 2012-13, but it proved to be Ferguson’s final season at the club and they have not challenged since.
Lewandowski remained at Dortmund for two more seasons, before making the move to Bayern Munich.
His career took off in Bavaria, and he has six Bundesliga titles to his name with the club – along with a Champions League crown.
And last week he was named FIFA’s Best Men’s Player for 2020 – beating the likes of Cristiano Ronaldo and Lionel Messi to the prize.
Lewandowski, 32, talked down comparisons with Ronaldo and Messi, but said he would happily share a table with the two greats of the game.
“Messi and Ronaldo have been sitting at the same table, at the top, for a very long time, and that’s what makes them incomparable,” Lewandowski said.
“That said, if you take the numbers for this year and even previous ones, I think I’m pretty good in terms of performance and goals scored.
“Failing to be at the same table as Messi and Ronaldo, I think I can invite them to eat at mine!”