Despite Zhou being the first full-time Chinese F1 racer, there has been speculation he does not come with major financial banking to incentivise Alfa Romeo to agree on new terms.
Speaking ahead of the summer break, Alfa Romeo F1 managing director Alessandro Alunni Bravi reckoned his squad wanted to retain its line-up of Zhou and Valtteri Bottas - who moved from Mercedes for 2022 on a two-year deal, but with an option to continue for 2024.
But there is competition for the seat. FIA F2 champion and Aston Martin reserve Felipe Drugovich - well backed by sponsors - and Alfa protege Theo Pourchaire are in contention.
Nevertheless, Zhou believes he is close to landing another deal, ideally for multiple seasons.
He said: “It's a little bit [more] delayed than I expected. But I think it’s just due to me, together with Alfa Romeo, trying to figure out these final details.
“In terms of, let's say, ‘Why don't you sign?’ I still have no answer to that. But we're definitely talking more into that and getting more close to being done.
“I'm happy to be together, spending more and more years together with this team. The future is bright for where the team is heading.”
Zhou pushed back on rumours that he lacks cash, saying: “I have personal sponsors and I don't know the rumours, but I don't feel I'm lacking any foundations on that side.
“It's not like the first contract you have in Formula 1 - everything's up to the team. The second one is a bit more into details.
“Nothing to be worried about majorly. I don't feel like what I show on track doesn't deserve to continue being in this paddock.”
Zhou added that his focus was on agreeing terms with his current team amid its Audi takeover, rather than chasing other vacancies.
He said: “At the minute [Alfa] is the priority. There's not a lot of seats that's available. I'm very keen on staying where I am.”
Elsewhere, there is also a seat potentially available alongside Alex Albon at Williams with the team yet to announce the future of American rookie Logan Sargeant.
Meanwhile, AlphaTauri has not officially tied down any drivers for 2024, meaning one of Yuki Tsunoda, Liam Lawson and Daniel Ricciardo will come onto the market.
Confirmed 2024 F1 grid (contracts):
Red Bull: Max Verstappen (2028), Sergio Perez (2024)
Mercedes: Lewis Hamilton (2025), George Russell (2025)
Ferrari: Charles Leclerc (2024), Carlos Sainz (2024)
Aston Martin: Fernando Alonso (2024), Lance Stroll (rolling)
McLaren: Lando Norris (2025), Oscar Piastri (2024)
Alpine: Esteban Ocon (2024), Pierre Gasly (2024)
Williams: Alex Albon (2024), TBC
Haas: Nico Hulkenberg (2024), Kevin Magnussen (2024)
Alfa Romeo: Valtteri Bottas (2024), TBC
AlphaTauri: TBC, TBC
