By the time Muhammad started his religion Jesus was already a legendary figure, known only from extremely biased sources.
Tom
At the times of Muhammad peace be upon him there were still people following the true teaching of Jesus peace be upon him and they later came to Islam.
That is because muhammad peace be upon him coming was known in the Injil.
This still can be seen in the bible too
John 16
5 But now I go my way to him that sent me; and none of you asketh me, Whither goest thou?
6 But because I have said these things unto you, sorrow hath filled your heart.
7 Nevertheless I tell you the truth; It is expedient for you that I go away: for if I go not away, the Comforter will not come unto you; but if I depart, I will send him unto you.
8 And when he is come, he will reprove the world of sin, and of righteousness, and of judgment:
9 Of sin, because they believe not on me;
10 Of righteousness, because I go to my Father, and ye see me no more;
11 Of judgment, because the prince of this world is judged.
12 I have yet many things to say unto you, but ye cannot bear them now.
13 Howbeit when he, the Spirit of truth, is come, he will guide you into all truth: for he shall not speak of himself; but whatsoever he shall hear, that shall he speak: and he will shew you things to come.
14 He shall glorify me: for he shall receive of mine, and shall shew it unto you.