Legere is "the perfect guy for the job," Sonnenfeld, a professor at Yale University and the founder of the nonprofit Chief Executive Leadership Institute, said on "Closing Bell."
"He's been very good at revivals and resuscitations," Sonnenfeld said, pointing to Legere's tenure at Global Crossing Ltd. after it was rocked by an accounting scandal in the early 2000s and his work building up "enormous" value at T-Mobile after AT&T dropped its bid to buy the wireless provider.
When asked by CNBC's Wilfred Frost if Legere would take the job, Sonnenfeld said, "I think he shouldn't, but I think he would."
"John would know how to shape something out of this," Sonnenfeld said.
T-Mobile didn't not immediately respond to a request for comment.
Sonnenfeld's remarks come just hours after Neumann said he was stepping down as CEO following controversy over WeWork's governance and valuation. The upheaval came as the coworking provider's parent company was heading toward an IPO.
Vice Chairman Sebastian Gunningham, who was previously an executive at Amazon, and CFO Artie Minson, formerly of AOL and Time Warner Cable, will assume the roles of co-CEOs, the company said. Neumann will be nonexecutive chairman.
Sonnenfeld said co-CEOs generally do not work, but he complimented Gunningham and Minson, calling them quality "stabilizers" on an interim basis.
In addition to his strong track record, Legere would be a good fit at WeWork because he has a relationship with SoftBank Group's Masayoshi Son, according to Sonnenfeld.
SoftBank and its associated Vision Fund is WeWork's largest external shareholder.
"It would be crazy for Masayoshi Son to not talk John into taking this job," Sonnenfeld said. "Whatever it takes."
"John would really know how to do this," Sonnfenfeld added.
Before joining T-Mobile in 2012, Legere was at Global Crossing for more than a decade, according to Bloomberg.
In late July, the Department of Justice announced it approved a merger between Sprint and T-Mobile, though a pending lawsuit has prevented the deal from going through.