Grosjean's departure after four years as a Lotus driver means the team - due to be taken over by Renault in the coming weeks - has one seat available as Pastor Maldonado has already been confirmed for next year.
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Reserve Jolyon Palmer, Jean-Eric Vergne and Kevin Magnussen are just a few of the names who have been linked with the vacancy.
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Assessing the situation, deputy team principal Federico Gastaldi said: "We know we can now publicly say 'bonne chance' to Romain who is headed to pastures new next year.
"He's been a real asset to us over the years, so we'll certainly miss him.
"We know we have Pastor confirmed for one seat, and we know there are quite a few tasty drivers available out there.
"We're doing everything to ensure we've got a desirable race seat, which needs to be filled.
"What happens next is there'll be a number of discussions in a number of places, then at some point we'll have an announcement to make."
Grosjean, who was unveiled by Haas on Tuesday on a multi-year contract that could lead to a Ferrari drive as early as 2017 given the American team's links to the Scuderia, is keeping the door open for a return to Enstone.
"I have to say the people at Enstone are the strongest group of people ever to keep pushing no matter what the circumstances. I had to think long and hard for the next step of my career," revealed the 29-year-old Frenchman.
"Part of my heart will absolutely always be with Enstone where I've grown and experienced so much over the years.
"I can remember turning up in September 2005 at the front gate, not speaking English and being very shy. Some of the people I met that day are still there.
"I'm turning a new leaf in my book, but it doesn't mean it's the end of the book, so why not come back to Enstone one day to become world champion with the team.
"Leaving Enstone at the end of the season won't be easy. I promised everyone some beers in December when I come to say goodbye to the factory.
"Until then we've five races left yet this season and I'm absolutely determined to end my time with the greatest high possible."
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