The Portuguese international was subject to a late loan bid from the Premier League champions who had failed in their efforts to sign Leighton Baines from Everton during the summer transfer window.
The season long loan move appeared to have been given the green light until Real Madrid pulled the plug on the deal at the last minute, concerned with their own lack of cover in that position after Guillerme Siqueira - who the club had lined up to replace Coentrao - opted to join Benfica over the La Liga giants.
Despite reports in Portuguese publication Record suggesting the 25-year-old was left devastated by the collapse of the move; Coentrao now insists he is happy where he is.
"There was the possibility of joining Manchester United, but I stayed at Real Madrid, and that's what matters," Coentrao told O Jogo.
"It would have been better if I had to stay despite having the chance to move to a better club, but that didn't happen as I already am at the best club in the world.
"I want to do better than I did last season, although I was at a very high level already. I want to show everyone that I deserve to be at Real Madrid."
Coentrao, who made his move to the Bernabeu from Benfica for €30m in 2011, is likely to remain behind Brazilian full back Marcelo in Carlo Ancelotti's defensive pecking order this season.
The Portuguese defender appeared set to leave the club this summer after Ancelotti admitted to the press the full back had asked for a move after being left out of the Real Madrid squad that took on Real Betis on the first weekend of the season.
The 25-year-old also found himself persistently linked with a move to Tottenham, with a number of reports throughout the summer suggesting he would be used as a makeweight in a deal to sign Gareth Bale before the Spanish giants eventually agreed to a £86m package.
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