This will be a short question and answer.
Open Theism is, broadly speaking, the teaching that God doesn’t know (or suspends his omniscience of) the future results of our free will. In other words God does not have foreknowledge of who will be saved when Christ returns and judges the living and the dead.
But, in short, the answer has to be ‘No’. Multiple passages in the Bible teach that God knows the end from the beginning, and even declares it (Isaiah 46:10).
“All who dwell one the earth will worship him, everyone whose name has not been written from the foundation of the world in the book of life of the Lamb who has been killed” Revelation 13:8
There is some potential ambiguity in the Greek word order about whether it is the book which was written before creation, or whether it was the Lamb killed before creation, but the similar passage in Revelation 17:8… “… Those who dwell on the earth and whose names have not been written in the book of life from the foundation of the world will marvel when they see that the beast was, and is not, and shall be present.” suggests that it was the book. Which completely goes against the idea of Open Theism.
However in as much as Open Theism is a reaction to another extreme, Calvinist Predestination, it has to be said that the teaching of the Bible is the God foreknows the result, but does not predetermine or predestine it.