During a round of town hall meetings, the boss spoke to staffers for reassurance and an update on the process, according to Deadline, which first noted the story.
The deal will see Disney gain key Fox assets including 20th Century Fox movie studio, 20th Century Fox TV studio and FX Networks.
Rice said the remaining assets are likely to simply fall under the name Fox. This includes Fox Broadcasting Company, national sports cable networks FS1 and FS2, Fox News Channel and Fox stations.
In the meantime, UK regulators are claiming that Disney will have to make a mandatory offer for all of Sky in the UK, as it completes the merger.