The forward spent a season each at Manchester United and then Chelsea between 2014 and 2016 but failed to make any impact, before returning to Monaco.
He managed just one goal in 10 top division appearances at Chelsea, nine of which were as a substitute in 2015/16, after having netted four times in 26 Premier League matches for Manchester United the season before.
On Monday he said he had no feelings of revenge when Colombia meet England in Moscow's Spartak Stadium but was ready to deliver a fine performance.
"It is true that I did not shine as I had wanted in England but that is part of the past," said the 32-year-old striker.
"Tomorrow's game I only can say that it is beautiful to be here to play against England and all our players are very well prepared."
"It is a game we always dreamed of playing. Since we were young children we wanted to play something like this," he said.
Colombia lost their Group H opener to Japan but beat Poland and Senegal to advance to the knockout stage.
England, however, had booked their knockout stage spot after two victories in their first two group matches, resting several players in their final group loss to Belgium.
"In England people will think their team are favourites. What we want to focus on is our skills and weapons and what we can do tomorrow," Falcao said.
"I am a dreamer, that's true, but on the other hand we have to take it step by step. That's the way we have done things here."
"Our first game was not that good and we faced the next two games as finals. Now we have the Round of 16 game. We need to try and do exactly what we have been doing until now."
(Reporting by Karolos Grohmann, editing by Neil Robinson)
