The centre-back also spoke highly of fellow Premier League team Arsenal as an attractive destination with his long-term future in France a doubt after an impressive season
The 22-year-old has helped guide Montpellier to the top of Ligue 1 this season and has previously been linked with a move to Newcastle United and Bayern Munich.
Yanga-Mbiwa also talked up the attraction of joining Arsenal this summer.
"To play for Manchester United would be a great satisfaction and a dream which could become reality," he told Canal+.
"Arsenal, also, is a big team. Marseille, also, despite of their difficulties, remains very attracting. I would never have thought that Marseille would follow me."
The centre-back's current deal is set to expire in the summer of 2013 and has featured heavily for La Paillade since joining on a youth contract in 2006.