Van Persie scored a hat-trick in the 5-3 win over Chelsea in the Premier League at the weekend, and Deschamps has issued clear instructions to his players so they can meet the threat head-on.
"Arsenal put in a great performance to score five goals against Chelsea," Deschamps told the press.
"They have a great attacking trio and of course Robin van Persie is in exceptional form.
"He's certainly one of the best players in Europe. What you want from a striker is to score goals, and his return is really impressive.
"But maybe he plays in a team that likes to help him; he has players like Gervinho and [Theo] Walcott who would rather pass to him than shoot.
"Maybe marking him is the best thing to do; we need to stop him getting the ball."
However, despite Arsenal's options, the former Juventus midfielder believes his men can stage an upset in London.
"A win would be amazing, but a point would also be a big achievement," added the Frenchman.
"The most important game might be our next one, at home to Olympiacos.
"Anything is possible. The most important thing for me and my players is to believe that we are capable of getting a result. That's what we need to focus on."
A win would see Marseille leap above Arsenal at the top of Group F.
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