Hosking also wants new chairman for airline
Flybe's largest shareholder wants an investigation into the recent takeover of the regional airline.
Hosking Partners is also seeking to replace chairman Simon Laffin with Eric Kohn.
The company, which operates several Isle of Man routes, was sold to a consortium including Virgin Atlantic and Stobart Group earlier this month.
Reuters reports Hosking owns an 18.72 percent stake in the company.