Twitter has approached CBS Interactive president and CEO Jim Lanzone and former Cisco CTO Padmasree Warrior as potential candidates for its CEO job, according to a Bloomberg report. The conversations with both executives happened as part of the company’s ongoing search for a replacement for former Twitter CEO Dick Costolo, who left the company at the end of June.

Jim Lanzone joined CBS Interactive as president and CEO in 2011, when the CBS unit acquired his online TV startup Clicker. Before founding Clicker, Lanzone spent seven years at Ask.com, serving as the company’s CEO from 2006 to 2008. Warrior served as Cisco’s CTO for seven years before leaving the company this July. Before her stint at Cisco, Warrior served as Motorola’s CTO for four years.

Twitter’s search committee has been looking at both internal and external candidates for the job. Twitter co-founder Jack Dorsey, who is currently leading the company as interim CEO, is seen as the likeliest candidate by many, and has been publicly backed by influential Twitter investor Chris Sacca. That’s why some of those external candidates apparently didn’t think they were under serious consideration, according to Bloomberg.

Twitter’s stock has been under pressure in recent weeks, at times sinking below the IPO price of $26 per share. Some of that can be attributed to the ongoing impact of the Chinese economy on the stock market, which also hit other tech and media companies hard, but the absence of a permanent CEO clearly hasn’t helped the company.