Context is important here, but Greek not so much (i.e. it adds nothing semantically that isn't conveyed din the English in this instance, and is in any case subservient to context, which is explicit).
First, to make it clear from the beginning, Jesus has already claimed to be the Christ, so 'I am not the Christ' is not one of the valid interpretations open to anyone here:
Matthew 16:13-20 (DRB)
And Jesus came into the quarters of Cesarea Philippi: and he asked his disciples, saying: Whom do men say that the Son of man is? 14 But they said: Some John the Baptist, and other some Elias, and others Jeremias, or one of the prophets. 15 Jesus saith to them: But whom do you say that I am? 16 Simon Peter answered and said: Thou art Christ, the Son of the living God. 17 And Jesus answering, said to him: Blessed art thou, Simon Bar-Jona: because flesh and blood hath not revealed it to thee, but my Father who is in heaven. 18 And I say to thee: That thou art Peter; and upon this rock I will build my church, and the gates of hell shall not prevail against it. 19 And I will give to thee the keys of the kingdom of heaven. And whatsoever thou shalt bind upon earth, it shall be bound also in heaven: and whatsoever thou shalt loose on earth, it shall be loosed also in heaven. 20 Then he commanded his disciples, that they should tell no one that he was Jesus the Christ.
Here, God the Father revealed to Peter that Jesus was "the Christ, the Son of the living God." And notice that there is a play on the true divine-prerogative identity of Jesus and Peter here respectively. If Peter is "Peter" then Jesus is also "the Christ." They mutually confirm each other's true identity.
Not to mention the same author introduces his Gospel thus:
Matthew 1:1 (DRB) The book of the generation of Jesus Christ, the son of David, the son of Abraham:
(If we don't trust him here, we should be pretending he relates the true words of Jesus, either.)
So back to our passage, then:
Matthew 24:3-5, 23-28 (DRB)
And when he was sitting on mount Olivet, the disciples came to him privately, saying: Tell us when shall these things be? and what shall be the sign of thy coming, and of the consummation of the world? 4 And Jesus answering, said to them: Take heed that no man seduce you: 5 For many will come in my name saying, I am Christ: and they will seduce many. ... Then if any man shall say to you: Lo here is Christ, or there, do not believe him. 24 For there shall arise false Christs and false prophets, and shall show great signs and wonders, insomuch as to deceive (if possible) even the elect. 25 Behold I have told it to you, beforehand. 26 If therefore they shall say to you: Behold he is in the desert, go ye not out: Behold he is in the closets, believe it not. 27 For as lightning cometh out of the east, and appeareth even into the west: so shall the coming of the Son of man be. 28 Wheresoever the body shall be, there shall the eagles also be gathered together.
So you see it's the false Christs who are to come in His name, claiming to be the Christ, not Him, the Christ. His point is 'you'll know when I've come alright, just as when everyone sees lightening; everyone will be gathered before me like vultures at a carcass!' (Cf. 2 Cor 5:10).