Kane, who will spearhead England Under-21s at the European Championship in the Czech Republic over the next two weeks, is a target for Louis van Gaal's side, who are expected to sell both Robin van Persie and Radamel Falcao.
But Fabrice Muamba, who made 33 appearances for England Under-21s and believes England have a realistic chance of reaching the final this year, has warned Kane to reject such overtures from Old Trafford.
"There is no point in going to United if you're not going to be the main man," he said. "At Spurs, he is the No1 player, he is the main guy right now. Unless he is sure that he is going to be the main man at United I would advise him to stay at Spurs and improve his career.
"It will be tough for Harry next season. To do what he has done in the Premier League year in, year out, takes a very strong talent. So we can assess Harry Kane much better next season to see where we are in terms of progress or whether he is a one-hit wonder."