Food-delivery company Postmates Inc. recently interviewed banks for roles on an initial public offering, which is likely to take place in the first half of 2019, according to people familiar with the company’s plans.

The company hasn’t yet selected underwriters but is expected to do so in the coming weeks, these people said. The company’s CEO and founder, Bastian Lehmann, has said Postmates is considering a 2019 IPO.

Postmates’...