Many believe that they will be. The atonement that Jesus Christ accomplished on the cross is both acceptable in the eyes of God and eternal for forgiveness and salvation. This means that the animal sacrifices themselves will not provide salvation to those who offer them. This should come as no surprise since that's what the Old Testament and the New Testament teach.
Consider these verses:
"What are your multiplied sacrifices to Me?" Says the LORD. "I have had enough of burnt offerings of rams, And the fat of fed cattle. And I take no pleasure in the blood of bulls, lambs, or goats (Isaiah 1:11).
For it is impossible for the blood of bulls and goats to take away sins (Hebrews 10:4).
The blood of Christ is the reality that the blood of animals symbolized. Consider the following passage found in Hebrews 9:13-14.
For if the blood of goats and bulls and the ashes of a heifer sprinkling those who have been defiled, sanctify for the cleansing of the flesh, how much more will the blood of Christ, who through the eternal Spirit offered Himself without blemish to God, cleanse your conscience from dead works to serve the living God? (Hebrews 9:13-14).
What then will be the purpose of the animal sacrifices during the Millennial kingdom?
One suggestion is that the animal sacrifices may be like a memorial (similar to the bread and wine at communion time). However they are used, it will be in a God honoring way (Psalm 51:15-19 and Heb. 11:4).(1)
The millennial system of sacrifices described by Ezekiel differs profoundly from the Aaronic system. It is not simply a reinstitution of Mosaic Judaism. Dwight Pentecost points out that there will be no ark of the covenant, tables of the law, cherubim, mercy seat, veil, golden lampstand, or table of showbread (Pentecost, pp.520-24)(2) . Instead of a high priest, a prince who has some royal or priestly powers will be on duty, but he will actually be neither king nor high priest. The levite's will have fewer Temple privileges, except for the sons of Zadok, who will serve as priests. The feast of Pentecost is omitted, as well as the Great Day of Atonement and the daily evening sacrifice.(1)
We won't know for sure what, if any, kind of memorial sacrificial system will be in place during the Millennial Kingdom until we get there. We do know that there will be a sacrificial system in place just before the second coming of the Messiah during the first half of the Tribulation Period. This will be approximately 3 and a half years before the Millennial Kingdom begins. We know this because the Anti-christ will put a stop to it. For more on this please read End To Sacrifice from the Daniel 9 prophecy.
The present-day re-established San Hedrin Court has purchased a herd of sheep for ritual sacrifice at the site of the Temple on the eve of Passover, when conditions on the Temple Mount permit. A member of the Sanhedrin, Professor Hillel Weiss, said in an interview that the symbolic Passover sacrifice is intended to remind Jews that the Temple rituals will resume when the Messiah comes.(3)
In Judaism, animal sacrifices are linked with the rebuilding of the temple. The rebuilt temple must be in place in order for the sacrifices to begin.
The presence and purpose of millennial sacrifices neither diminish the finished work of Christ, nor violates the literal interpretation of the prophetic passages found in Ezekiel 40-48. The millennial temple and its ritual will serve as a daily reminder of fallen man's need before a holy God and lessons about how this same God lovingly works to remove the obstacle of human sin for those who trust Him.(4)
1). John Whitcomb writing for The Popular Encyclopedia of Bible Prophecy by Tim Lahaye:
2). Things to Come by Dwight J. Pentecost:
3). Haaretz-Israel News 2-28-2007.
4). Midnight Call Magazine. (Dr. Thomas Ice) September 2007 p.29.