Steiner has confirmed a decision to let Grosjean and Magnussen leave at the end of this season was arrived at "two or three weeks ago", and the drivers then informed last week.
There are now a few options open to Steiner and team owner Gene Haas for replacements, notably F2 race-winner Nikita Mazepin given the money behind the 21-year-old Russian, and Sergio Perez who brings him with considerable sponsorship from Mexico.
Also in the frame are Ferrari academy drivers Mick Schumacher, Callum Ilott and Robert Shwartzman.
The Scuderia's placement of current F2 championship leader Schumacher, in particular, depends on whether it opts to retain Antonio Giovinazzi at Alfa Romeo alongside Kimi Raikkonen, and should the Finn also choose to remain in F1 for another season.
Asked whether he was looking for a driver with money, Steiner replied: "We could be - money and talent. Talent always needs to be there, not only money, talent is more important.
"Some people have sponsorship they bring with them. We are looking at all the options out there."
Steiner has made clear he and owner Gene Haas are in no rush to make a decision, suggesting outside factors such as Ferrari's influence and the possibility of Perez needing to secure his backers from Mexico could come into play.
"It's a mix of it," added Steiner. "We have got quite a few things we can choose from and opportunities.
"There are quite a few opportunities out there and they're not going away because the market is pretty small this year and we have lucked into that one this year.
"So that is the reason why we are not in a hurry to make an announcement."
Steiner has insisted the team will take its time "to evaluate everything properly and make a good decision".
He added: "The longer you have to think about a decision it normally gets better and you have more clarity.
"We are in no hurry so why should we have to do it tomorrow or the day after tomorrow? It takes as long as it takes until we are confident and happy with the decision we are going to make."
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