The reports come less than a week after vice president of communications Sean Garrett tweeted to announce his exit from the company.
Kramer, who joined from stock trading platform e-trade to become Twitter’s vice president of consumer marketing, was charged with making the social network more appealing to “mainstream” consumers as it looks to grow a broader base of advertisers.
Garrett and Kramer were both responsible for appointing Twitter’s first PR agency, Edelman, for a short-term project.
The company is forecast to generate almost $140m (£88m) in global ad revenue in 2011, up 210% year on year, according eMarketer. Sky became Twitter’s first UK advertiser in September.
Twitter declined to comment about Kramer’s exit.