Prior to World War I, the Middle East was part of the Ottoman empire, so there were no Arab states, apart from Egypt. After World War I, the Middle East came under British and French Mandates, so once again there were no Arab states. In any case, Palestine was not the property of other states to sell.
However, during the first half of the twentieth century, Jewish immigrants did buy up Palestinian farmland from both Turkish landlords and from the Palestinians themselves. When the Palestinians began to realise that these purchases were intended by the Jews as not only transfer of property rights, but also of sovereign rights, many Palestinians unsuccessfully opposed further sales of farmland to the Jews.