No, Moslems do not believe Jesus was the Messiah.
Yes they do!
YUSUFALI: Behold! the angels said: "O Mary! Allah giveth thee glad tidings of a Word from Him: his name will be Christ Jesus, the son of Mary, held in honour in this world and the Hereafter and of (the company of) those nearest to Allah;
PICKTHAL: (And remember) when the angels said: O Mary! Lo! Allah giveth thee glad tidings of a word from him, whose name is the Messiah, Jesus, son of Mary, illustrious in the world and the Hereafter, and one of those brought near (unto Allah).
SHAKIR: When the angels said: O Marium, surely Allah gives you good news with a Word from Him (of one) whose name is the '. Messiah, Isa son of Marium, worthy of regard in this world and the hereafter and of those who are made near (to Allah).