Both Grosjean and his teammate Kevin Magnussen are talking to IndyCar teams about drives in 2021 after being dropped by Haas.
Grosjean insists he has high hopes of landing a seat, despite only a few being available, although Magnussen is less optimistic about his own prospects.
Grosjean had previously expressed reservations about racing on ovals, but with the final calendar featuring only three, he says he's willing to take on the challenge.
"I thought that IndyCar has more ovals that it actually does," he said. "Ovals are something that I'm not necessarily a huge fan of, but looking at the calendar there are basically three ovals, Texas, which is fast, the Indy 500, and one other short track, I don't remember the name.
"Obviously racing the Indy 500 is something unique, it's one of the top three races in the world with Le Mans and Monaco.
"I think you can put your fear aside a little bit and go for it, and accept that the cars are much safer, the walls are safer, it's just all moved in the right direction.
"It's gone in a way that I can accept that it can be a good opportunity and a fun experience, and hopefully a successful experience."
Grosjean is adamant that he can still find a seat for next year.
"There are opportunities left and looking at what we can do and how we can do it, there are some wishes from both sides to make it happen, which is nice, and some good challenges.
"If you look at Penske and Chip Ganassi, which I guess are the two top teams in IndyCar, they are fully booked. But you would not necessarily expect to land on one of those seats when you go to IndyCar, you need to prove that you can race in that series.
"I spoke with Simon Pagenaud recently, and also Marcus Ericsson. Marcus has been really helpful, because he knows Europe, he knows GP2, he knows F1, and he knows the US as well. Let's see what coming, I'm hoping in the next few days, and then we can look at details and so on."
Grosjean acknowledged that the remaining available drives are with teams that would probably require a driver to bring a budget.
"I think motorsports is changing generally," he said. "And I wouldn't be surprised if now drivers around the world need to have sponsors that want to follow them.
"Jimmie Johnson is a good example in IndyCar, but also some others, where you present an image, and the companies behind the image are happy that you represent it, and you move forward."
Regarding his prospects, Magnussen admitted that he was running out of time.
"I've been speaking to teams and seeing what is possible," said the Dane. "We're a little bit late in the year, a lot of teams have already got drivers for the future. I don't think it looks likely for next year, for sure. I don't see any reason to tell you who I'm talking to, but some good ones."