The goalkeeper, who is filling in for the injured Igor Akinfeev, insists his side will not play negative football as they look to seal a place in the quarter-finals of Euro 2012
Dick Advocaat's side need only a point to be sure of their progress while the Greeks must win to stand any chance of reaching the quarter-finals.
At the same time, Czech Republic and Poland will be in action in what is set to be a winner-takes-all clash, although the former could afford a stalemate.
Malafeev, though, refutes the idea of Russia simply going out to gain the point they need and believes his side could regret using such negative tactics in this situation.
"To plan to play for a draw means limiting your chances. If you do that, you have the choice of two possible results, you either get yours and draw or you lose," the Zenit St Petersburg man told reporters.
"But in general in football there are three possible results. So, even by elementary logic, it is dangerous to aim for a draw."
Russia have opened the scoring in both of their group games so far, and the 33-year-old believes that they will need to continue this trend if they are to beat the Greeks.
|14/1||Russia are 14/1 to beat Greece 3-0 with Paddy Power|
In Euro 2004, Russia had already finished bottom when they entertained eventual winners Greece in their last group game and proved to be the only side to beat them in the competition as they secured a 2-1 victory.
Malafeev believes there are a lot of unique qualities about the Greeks and even though they are not likely to re-create history again this summer, he revealed how he was cheering them on once his own nation had been eliminated.
"[In 2004] after we beat them, I strongly supported the Greeks. I was really glad when they won the tournament," he added.
"They are organised, they play from defence, using long balls to their tall forwards. They also distribute the ball well from the middle of the pitch and can counter attack with pace on the wings."
Russia and Greece kick off at 20:45CET on Saturday.