Sir Christopher Hohn, who runs the Children’s Investment Fund which owns 5 per cent of the LSE, and has called for the resignation of LSE chairman Donald Brydon.
The LSE said it has followed the “proper process” to replace Mr Rolet.
It said in a statement at the time: “LSE has followed a proper governance process to plan an orderly succession for the CEO.
“The FCA [Financial Conduct Authority] was kept informed throughout the process and emphasised the importance of the plan for an orderly succession.
“Xavier Rolet will be providing input into the process to identify his successor and is focused on his role as CEO until his successor is appointed.”
Mr Hohn said: “It is our belief that the majority of shareholders support the CEO staying.
“It is imperative that we now hear directly from Xavier Rolet.”
LSE announced on 19 October that Mr Rolet would step down at the end of next year, just under a decade after he took charge and transformed the company with a string of deals.