Motorsport.com understands Martini discussed an extension with Williams as well as speaking to other teams about an alternative arrangement.
But it is believed the board of the Bacardi Group, of which Martini belongs, decided to stop diverting resources to F1 entirely as it no longer aligned with its strategic objectives.
When asked to comment, deputy team principal Claire Williams told Motorsport.com: "We have discussed extending beyond 2018.
"While we would both like to do so, the Bacardi Group have told us that they will step away entirely from Formula 1 when our contract expires at the end of this year.
"They have many brands to support and obviously their strategic priorities evolve over time."
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