Kane took the Premier League by storm last season as he scored 21 goals and was voted the PFA Young Player of the Year.
He said: “Of course I have been watching Sky Sports and have seen the interest.
“But I am happy at Spurs and I look forward to the future with Spurs. I have seen there is interest but that’s all I know. It is flattering for other clubs to maybe be interested.”
Asked if it would be difficult to resist the lure of a ‘big club’ move, he said: “Tottenham are a big club and that’s how people have got to see it. I’m at a big club now and enjoying my football looking forward to next season at White Hart Lane.”
Kane started for England as they lost 1-0 in their opening European U21 Championship match against Portugal on Thursday night.
United are in the market for a new striker after electing to sever ties with Radamel Falcao while Robin van Persie’s future at Old Trafford remains uncertain.