From R. Shlomo Aviner (link):
Q: Is it true that the Messiah has already arrived?
A: No, since the Messiah is the King of Israel who is involved with Torah, leads the Nation according to the Torah, and leads us in war (Rambam, Hilchot Melachim 11:4), and we have yet to reach this point.
Q: When will the Messiah arrive?
A: It is forbidden to make calculations (Rambam, Hilchot Melachim 12:2). We wait every day.
UPDATE: More on this subject from R. Aviner: link