The 26-year-old has made 255 senior appearances for United and is a key player at Old Trafford.
“You look at it as a step down if you leave,” said Fletcher.
“If you are lucky enough to stay, you will have played at the top for your whole career and it does not get much bigger than Manchester United.
“Players who left say, ‘think twice before you leave, because there is nowhere like Manchester United.’
“Everything about the club makes it the place you want to be. No-one really thinks about leaving when you are here.”
