After two seasons in Formula 1, Schumacher has failed to set the world alight despite entering the sport with strong junior pedigree.
A difficult car through 2021 meant any potential was hidden, but heavy crashes and being beaten by Magnussen this season have not helped his chances.
“Expect the announcement sometime next week,” Steiner confirmed.
“I'm not telling you a day because then everybody will be starting, waiting for that day.
“It will be coming next week.
“We are just sorting out details [about] how are we going to do what we are going to do,” he added.
Haas was in the headlines on Friday for an entirely different reason, when Magnussen secured the team's first-ever pole position.
The Dane made the most of the conditions and the right tyre choice by the team in Qualifying to secure top spot.
It will see him start from pole position for the Sprint and be formally recognised as a pole-sitter regardless of how he fares in the Saturday afternoon session.
“It's fantastic for the team that, for me, is the most important thing,” Steiner said, having had a night to dwell on the success.
“These guys believed in it, they always worked hard.
“It's the same hard work when you have no success as when you have got success.
“We got the pole position, the first for Haas F1 – hopefully not the last.
“Everybody did a fantastic job yesterday.”