The 21-year-old has attracted interest from various quarters since joining the Scottish club from Beerschot AC in 2011, with United the latest club to be linked with the Kenyan.
However, he told SuperSport: "I have heard a lot about my intended move to several clubs, the latest being Manchester United."
"Personally I just think those are rumours. My focus now remains with my team Celtic, whom I want to help in both the domestic competitions and Champions League.
"Leaving Celtic will not be easy. They cannot just let me go as easily as many people think they will. All in all am happy here and looking forward to continue playing for them as I work hard in my career."
Wanyama's contract expires in 2015.