Team chief Gunther Steiner said on Thursday Haas may choose two rookies to replace departing drivers Romain Grosjean and Kevin Magnussen, but they will take their time to decide.
Speaking ahead of this weekend's Portuguese Grand Prix and after the Frenchman and the Dane had confirmed their exits on social media, Steiner revealed the drivers were informed last week.
"We wanted to be fair to them," he said. "We could have kept it for us for a while and then just done it, but these guys were good with us in the last years.
"We said we're not going that way. We're going to do some changes and therefore we want to tell them -- so they've got a chance to find something else."
He said the team had made a decision to part company with the duo "two or three weeks ago".
He said they were "very understanding".
"They weren't happy -– who would be? But they had a good understanding and they know that we gave them a good run at it as well."
Steiner added the team had not made any decisions on a replacement driver line-up and would not comment on suggestions that rookies Mick Schumacher, the 21-year-old son of seven-time world champion Michael Schumacher, and Nikita Mazepin were leading candidates.
Both have commercial backing, which he admitted was an attractive factor.
"Talent always needs to be there," he said. "Not only money. So talent is very important, or more important, but some people have got sponsorship they bring with them. So we are looking at all the options."
He suggested that running two rookies may be preferable to taking an experienced driver alongside a rookie.
"If you have a very good experienced one and a rookie who finds it difficult, he loses his confidence. Is that good?
"No. Look at what happened to a lot of people who were in the same team (Red Bull) as Max (Verstappen). They all struggle because he is so good. Maybe two rookies is a good thing. I don't know."
If the team consider an experienced driver it could be a choice between Sergio Perez, whose Mexican fan-base and backing would make him an attractive prospect, and German 'super-sub' Nico Hulkenberg.
- Magnussen attracted by IndyCar -
Denmark's Magnussen, who also had spells at McLaren and Renault, joined Haas in 2017 but has only scored one point so far this year.
He has repeatedly expressed an interest in racing in the IndyCar Series.
"I haven't won a race in seven years and that won't happen in 2021 if I continue in F1," he told Danish daily BT. "That's why I'm looking for new challenges in other categories."
Grosjean, who claimed 10 podium finishes earlier in his career at Lotus, posted his first points of the season with a ninth-placed effort in the Eifel Grand Prix earlier this month.
The 34-year-old has hinted that he could join the World Endurance Championship or Formula E.
Haas head into the final six races of the year ninth in the constructors' standings, above only pointless Williams.