The obvious destination for the youngster is Ferrari-powered Haas, who have a co-operation agreement with the Italian team and also share the Briton's services as a reserve.
Bearman jumped into the Ferrari for final practice and qualifying in Jeddah last Friday after Carlos Sainz (29) had surgery for appendicitis, qualifying 11th and then finishing seventh on Saturday.
At the same time Haas, who slumped to last overall in 2023 and replaced Guenther Steiner with Japanese engineer Komatsu, scored their first point of the campaign with Nico Hulkenberg (36) finishing 10th.
Komatsu said that was like a win for Haas but Bearman's achievement was also noted.
"Last year when we ran him in FP1 (first practice) sessions in Mexico and Abu Dhabi straight away it was obvious that he’s a total package, he’s so impressive," he told Sky Sports.
"So I was very happy that we got him for six FP (practice) runs this year and very happy for him," he added of the youngest ever British F1 driver.
Hulkenberg and teammate Kevin Magnussen (31) are out of contract at the end of the season.
Bearman said after the race he was looking forward to building up a relationship with Haas and getting more laps in.
"I hope I did a good job interview today," he said.
FORMULA TWO
The Briton also has a Formula 2 campaign to think about, with no points on the board so far due to missing the Jeddah round - despite taking pole position for the feature race - while Barbadian Zane Maloney (20) leads the standings with 47.
Ferrari boss Fred Vasseur said F2 had to be the main focus for the youngster for the rest of the season.
A second Formula 1 outing in Melbourne in two weeks' time cannot be completely ruled out, however, and depends on Sainz's recovery.
"We’ll take a decision probably only in Melbourne," said Vasseur. "At least we know that with Ollie we have also a good reserve."
Sainz will rest and recover this week and can be counted on to make every effort to be in the car in Australia, having dragged himself out of hospital a day after his operation to attend the race at the Corniche circuit.
The Spaniard has already shown, however, that hope is not always enough.
"He struggled a lot on Thursday in both sessions with a fever and stomach issues and at the end, he was convinced that it would be much better the day after," recalled Vasseur.
"The day after he called me in the morning and said he would be here for the quali for sure. At 11:30, he was in the hospital and it was quite clear we were not going in the right direction."
