A lacklustre growth combined with a recent large stock sale by Rowghani have prompted the microblogging service to evaluate the need of a COO, Re/code said, citing sources.
Chloe Sladden, Twitter's North America media head, who reports to Rowghani, has been reorganizing her unit and she may be preparing to leave the company, the website said.
Representatives at Twitter did not immediately respond to an email seeking comment.
Twitter's first-quarter results in April revealed slowing momentum at the company that exuberant investors just six months ago had argued could one day match Facebook's scale.
Last month, research firm eMarketer said Twitter is seeing strong user growth in the Asia-Pacific region, helping the messaging platform compensate for a slowdown in the US and Europe.
The report by eMarketer forecasted that Twitter's global user base will increase 24.4 percent in 2014, led by big gains in countries such as Indonesia and India, and to a lesser extent Argentina, Mexico and Brazil.
The research firm said its figures on current Twitter usage are lower than company estimates 183 million at the end of 2013 "because we rely heavily on consumer survey data to weed out business accounts, multiple accounts for individual users and other sources of potential double-counting."
Twitter in April estimated the monthly active users at 255 million, which led to a slump in its share price because it suggested sluggish growth.
The eMarketer report said Twitter's worldwide users will hit 227 million this year, and nearly 400 million by 2018.
Written with agency inputs