WeWork’s parent is expected to postpone its initial public offering after investors questioned how much the company is worth and raised concerns about its corporate governance.

The shared-workspace company—which had planned to begin a roadshow to market the shares as early as Monday ahead of a trading debut next week—is likely to shelve the offering until at least next month, people familiar with the matter said.

The move reflects the difficulty the company, along with its co-founder and chief executive, Adam Neumann, have had getting the offering off the ground, even after dramatically slicing its valuation and revamping its governance.

It is a blow for a company that had been one of the most richly valued of a raft of startups planning to go public in a banner year for IPOs, but has been dogged by doubt over whether it can thrive as a public company.

We Co., as the company is officially known, had been valued at $47 billion in a fundraising exercise this year with SoftBank Group Corp. , but in recent days its executives and underwriters had become resigned to something closer to between $15 billion and $20 billion or possibly lower, people familiar with the matter said.

The company also spelled out a series of governance changes, including adding a lead independent director and ratcheting back the potency of Mr. Neumann’s supervoting rights.

Still, those changes don’t appear to have assuaged investors who questioned Mr. Neumann’s outsize control and the hundreds of millions of dollars he has reaped from selling his shares and other transactions with the company.