The pressure follows signs that outside investors do not value the much-hyped firm as highly as SoftBank did when it invested last year.
SoftBank had valued WeWork at about $47bn (£38bn).
But an upcoming share offering could put the firm's worth below $20bn, as investors question WeWork's opaque corporate structure, governance and profitability.
Is WeWork really worth nearly $50bn?
A lower valuation would be a blow to SoftBank, forcing it to write-down its investment. The Financial Times said SoftBank was worried that a low price would affect its other fundraising projects.
But on Tuesday, CNBC reported that WeWork intended to forge ahead with its roadshow, in which the company pitches itself to potential investors.
SoftBank chief Masayoshi Son has praised WeWork, arguing that its profitability will surge after a period of loss-making expansion.
But critics say WeWork's model could leave it vulnerable during an economic downturn.
The company rents office space for the long-term, subletting that space to firms and individuals on more flexible lease terms. That could leave it on the hook for lease payments even if tenants grow scarce.
WeWork has also faced questions about its complicated financial ties to founder chief executive, Adam Neumann, who would retain voting control of the company.
Last week, Mr Neumann returned $5.9m worth of stock to the firm, which he had controversially received in exchange for his trademark of "We".
Concerns about slowing global growth could also contribute to a bumpy ride in the public markets, as seen in other high-profile offerings this year, such as Uber.
Since WeWork's start in New York in 2010, it has expanded to more than 500 locations in 111 cities across 29 countries.
The growth has been costly. WeWork lost about $1.6bn last year, despite revenue nearly doubling.