Aston Martin say they want to keep Fernando Alonso beyond the end of his current contract, which runs until the end of 2024.
The Spaniard, 42, has scored eight podiums for Aston Martin this year.
Team principal Mike Krack said at the Abu Dhabi Grand Prix he was “surprised to be asked the question” after such an impressive year by Alonso.
Krack added that he had no concerns about Alonso’s age – the two-time world champion will be 43 next July.
Alonso has said that he has not yet decided whether to continue racing in F1 beyond the end of next season.
He said on Thursday at the Abu Dhabi Grand Prix that his 2023 season had been the best of his career after 2012, when he was at Ferrari and took the fourth fastest car on the grid to the brink of the world title before missing out at the final race.
He added that he was not concerned about losing his speed in the near future but that the increasingly congested F1 calendar would be a consideration.
“I said many times even before (the first time I left F1 in 2018) that the day I will stop racing is not because I will feel not motivated for driving or I feel slow,” Alonso said.
“If I feel slow one day I think it will be noticeable and I will be not happy with my performance and I will be the first one to raise my hand and say this is time.
“But I don’t think that time will arrive, honestly, in terms of feeling slow, because I have extreme self-confidence in my performance.
“But it could be that with the calendar and with the demanding schedule I will feel it is time because there are other things in life.
“It has been a very demanding season only with 22 races, with two cancellations.
“Next year, with 24, the proper calendar, we have to see how it feels.
“Even Las Vegas I saw today that it is a triple header (the first of three races on consecutive weekend at the end of the season). These kinds of things will drain my battery, not driving.”
He added: “I cannot say anything on my future now.”
