But McLaren is making clear it wants to keep him.
"We will do everything we can to keep Fernando," said managing director Jonathan Neale.
Alonso's options actually appear limited, with Mercedes, Ferrari and Red Bull apparently having no vacancies.
Renault is one option for the 36-year-old, but another may now be emerging - Williams.
"Auto Motor und Sport call it a rumour, but at Auto Bild Motorsport we know that Williams and Alonso are on the brink of a sensation," the German publication said.
"The two sides have been talking for some time."
He would presumably take Felipe Massa's place, as Williams is yet to commit to the veteran Brazilian for 2018.
"There's no reason not to go for another year if the package is right," Massa said at Spa. "But I'm completely relaxed, no matter what happens."
An Alonso-Williams collaboration makes sense, as the British team is eyeing a return to regular podium places, considering deepening its relationship with Mercedes, and looking to keep sponsor Martini happy with an experienced driver.
And sources report that Lance Stroll's billionaire father Lawrence is also keen on Alonso joining Williams, as his 18-year-old son could learn a lot from the two-time champion.
Auto Bild claims: "Lawrence Stroll is willing to pay Alonso's EUR 25 million salary personally, as he wants the best driving instructor and development aid for his son.
"Stroll even plans to take over the Williams team, having already invested at least EUR 40 million," the report added.
McLaren could replace Alonso with 17-year-old British youngster Lando Norris, who has reportedly already begun a series of private F1 tests.
"McLaren is letting him drive at every opportunity," an insider said.
Finally, another option for Alonso may be Force India.
"We would be the ideal team for him," said sporting director Otmar Szafnauer.