Kenya's government had earlier indicated they were in talks for an amount of $750 million, but it has since been bumped up, the document showed.
The lending instrument is a Development Policy Operations loan, which is tied to a pre-agreed policy area.
Kenya qualified for that type of financing in 2019 and it has since received four such loans, the last one in March.
The East African economy is grappling with many challenges, including a heavy debt load, lack of fiscal space, drought and a weaker currency.
The loan still requires the approval of the bank's board. It is expected to make a decision before the end of Kenya's current financial year on June 30.
Neither the government, nor the World Bank, responded to requests for comment.
