The French striker has been in decent form for the Red Devils this season but his future has become something of a source of speculation in recent months because he has been in and out of the first team.
The 22-year-old has scored nine goals and made five assists in 26 Premier League appearances for the Red Devils this season to help them up into second place in the top-flight table.
He also netted once in the Champions League before Manchester United were knocked out by Sevilla after a surprise defeat in the last 16.
There have been suggestions that Martial could be on his way out of Manchester United recently and he was linked with a potential move to Arsenal in the January transfer window.
However, Burley feels that Martial is likely to stay at Old Trafford beyond the summer, and he is tipping the striker to have a solid World Cup for France in Russia.
Speaking to ESPN FC, Burley said: “I think he will stay. Martial could have a good World Cup for France.
“If they can get the consistency level out of him, then he is a match-changer and game-winner.
“For that reason, I am going to say [he will] stay. You need players who are willing to come off the bench.”
Manchester United return to Premier League action on Saturday when they take on Swansea City at Old Trafford in front of their home fans.
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