Slot said on Thursday that he wanted to succeed German Jurgen Klopp as Liverpool manager.
Feyenoord and Liverpool have held positive discussions and only the final details need to be decided for Slot to join the English club, Dutch newspaper AD reported.
Liverpool hope to complete the negotiations this weekend, the report added.
The clubs have also agreed on the compensation fee Liverpool will pay to Feyenoord, Dutch and British media reported later on Friday.