Yes, but let me qualify that at the end of my answer.
2 Nephi 25:7-8 teaches:
[Nephi is speaking] But behold, I proceed with mine own prophecy
… Wherefore, they are of worth unto the children of men, and he
that supposeth that they are not, unto them will I speak particularly
… for I know that they shall be of great worth unto them in the
The Book of Mormon was specifically written for the last days or last dispensation of time. From D&C 112:30:
For unto you, the Twelve, and those, the First Presidency, who are
appointed with you to be your counselors and your leaders, is the
power of this priesthood given, for the last days and for the last
time, in the which is the dispensation of the fulness of times....
The Book of Mormon contains a prophecy of one Zenos, describing the Lord's efforts to gather His people in the last days. That prophecy is found primarily in Jacob 5, but from a summary in Jacob 6:2 we read:
And the day that he shall set his hand again the second time to
recover his people, is the day, yea, even the last time, that the
servants of the Lord shall go forth in his power, to nourish and prune
his vineyard; and after that the end soon cometh.
And we believe we are called to perform missionary work because this is the last time before the Second Coming when that can happen. From D&C 43:28 we read:
Wherefore, labor ye, labor ye in my vineyard for the last time—for the
last time call upon the inhabitants of the earth.
So, yes, we believe we are living in the last days before our Lord's second coming.
We are strong believers in the Lord's disclaimer (Matthew 24:36):
But of that day and hour knoweth no man, no, not the angels of heaven,
but my Father only.
Which is reiterated in D&C 39:21:
For the time is at hand; the day or the hour no man knoweth; but it
surely shall come.
We know these are the last days. We do not believe anyone knows or can calculate when His coming will be. Since we believe our Heavenly Father, His son Jesus, and the Holy Ghost are three separate individuals, we believe that Jesus' words as recorded in Matthew mean that even He (Jesus) does not know when He will return. Only our Heavenly Father knows.
It is for this reason that LDS Church leaders teach we should basically live each day as if it were our last. President Henry B. Eyring taught:
The scriptures make the danger of delay clear. It is that we may
discover that we have run out of time. The God who gives us each day
as a treasure will require an accounting. We will weep, and He will
weep, if we have intended to repent and to serve Him in tomorrows
which never came or have dreamt of yesterdays where the opportunity to
act was past. This day is a precious gift of God. The thought “Someday
I will” can be a thief of the opportunities of time and the blessings
Finally, please note there are many verses in the Book of Mormon and the book of Doctrine and Covenants that support this belief. I've provided only a fraction of them here.