The Kingdom is an everlasting Kingdom, Psalm 145:13.
This is the basis for our Kingdom eschatology.
No Millennium could fulfill this, for Millenniums end. No earthly thing will suffice, because, regardless of whether you think the New Heaven and New Earth are completely new, or simply the old one re-done, it, too, must end when the sun is consumed.
The Kingdom is a spiritual Kingdom, because it is an everlasting one. God’s Kingdom will endure, though heaven and Earth will pass away. Though they will pass away one day, Jesus’ words, and hence, His Kingdom, for He talked about His Kingdom, never will.