There's a possibility that it will take quite a bit of time to complete the documents.
ご質問ありがとうございます。
この場合、「書類が[完成](https://eikaiwa.dmm.com/uknow/questions/34520/)するまでに時間がかかるかもしれません」と言いたいなら、英語で「There's a possibility that it will take quite a bit of time to complete the documents.」と言えます。
ご参考になれば幸いです。
It might take some time until the paperwork is completed.
"書類が完成するまでに時間がかかるかもしれません"
- It might take some time until the paperwork is completed.
- It may take some time before I can complete the paperwork.
- It will take a little more time until the paperwork can be completed so please wait a little longer.
アメリカ合衆国 
