Haas, who will use Ferrari engines, scheduled a news conference for a driver announcement next Tuesday Sept. 29 at their Kannapolis, North Carolina, headquarters.
Grosjean and Mexican Esteban Gutierrez, who drove for Swiss-based Sauber in 2013 and 2014 and is now the Ferrari reserve, are seen as frontrunners to race for Formula One's first American team since 1986.
Haas has said his dream lineup would be a driver from the Ferrari squad and another with F1 race experience.
Grosjean, whose British-based Lotus team have severe financial problems but are hoping to be bought by Renault, told reporters at the Japanese Grand Prix he had made his decision but was coy about the details.
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"It should be sooner rather than later," he said on Thursday when asked when news might be announced, adding it would probably be next week.
"In my mind, it's done. I'm happy with it. You will know soon.
"You can always change your mind but I think I am pretty pleased with my choice."
Haas, whose founder and chairman Gene Haas is co-owner of the successful Stewart-Haas NASCAR team, appear to have ruled out naming an American driver for their debut season.
"There is nobody out there at the moment," team principal Guenther Steiner told the official formula1.com website this month, before Californian Alexander Rossi was drafted in by Marussia for five of the last seven races.
Rossi, 23 and currently second in the GP2 support series, made his grand prix race debut in Singapore last weekend and finished 14th.
The new team will have bases in three countries -- a headquarters in Kannapolis, race team factory in England and a design and aerodynamics department in Italy.
(Reporting by Alan Baldwin, editing by Ken Ferris)
