Why could't you remove the grate using an angle grinder and then use a pvc donut inside the existing cast iron?Floor drains usually consist of a drain body that is embedded in the floor and the grate is attached to it. This makes removal next to impossible unless you tear into the floor.
There is a possibility that you have a push on grate and replacements are likely available. But even these may require a slight amount of concrete demo.
I can't give more suggestions without seeing it though.